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Leases - Schedule of Components of Leases (Detail) - USD ($) $ in Millions	Jun. 24, 2023	Jun. 25, 2022
Leases Commitments And Contingencies [Abstract]
Operating lease right-of-use assets	$ 49.0	$ 61.2
Operating lease liabilities	9.0	7.6
Operating lease liabilities, long-term	42.4	51.5
Total operating lease liabilities	$ 51.4	$ 59.1

X

- Definition

Leases, Commitments and Contingencies.

+ References

No definition available.

+ Details

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Namespace Prefix:	syna_
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Balance Type:	na
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X

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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Balance Type:	credit
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- Definition

Present value of lessee's discounted obligation for lease payments from operating lease, classified as noncurrent.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

+ Details

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Balance Type:	credit
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- Definition

Amount of lessee's right to use underlying asset under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 842
-SubTopic 20
-Section 45
-Paragraph 1
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=123391704&loc=SL77918627-209977

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