Theorem tposresxp

Description: The transposition restricted to a Cartesian product. (Contributed by Zhi Wang, 6-Oct-2025)

	Ref	Expression
Assertion	tposresxp	|- ( tpos F |` ( A X. B ) ) = tpos ( F |` ( B X. A ) )

Proof

Step	Hyp	Ref	Expression
1		relxp	|- Rel ( A X. B )
2		tposres	|- ( Rel ( A X. B ) -> ( tpos F |` ( A X. B ) ) = tpos ( F |` `' ( A X. B ) ) )
3	1 2	ax-mp	|- ( tpos F |` ( A X. B ) ) = tpos ( F |` `' ( A X. B ) )
4		cnvxp	|- `' ( A X. B ) = ( B X. A )
5	4	reseq2i	|- ( F |` `' ( A X. B ) ) = ( F |` ( B X. A ) )
6	5	tposeqi	|- tpos ( F |` `' ( A X. B ) ) = tpos ( F |` ( B X. A ) )
7	3 6	eqtri	|- ( tpos F |` ( A X. B ) ) = tpos ( F |` ( B X. A ) )