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Supplemental Financial Statement Information - Schedule of Non-Current Other Assets (Details) - USD ($) $ in Millions	Jun. 28, 2025	Jun. 29, 2024
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Prepayment of intangible assets	$ 139.3	$ 42.5
Right-of-use assets	45.2	46.8
Other	32.6	47.5
Non-current other assets, total	$ 217.1	$ 136.8

X

- Definition

Other Noncurrent Assets

+ References

No definition available.

+ Details

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Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Prepayment Of Intangible Assets

+ References

No definition available.

+ Details

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Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Right-Of-Use Assets, Noncurrent

+ References

No definition available.

+ Details

Name:	syna_RightOfUseAssetsNoncurrent
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- References

No definition available.

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- Definition

Amount of noncurrent assets classified as other.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(17))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

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