Theorem tposid

Description: Swap an ordered pair. (Contributed by Zhi Wang, 5-Oct-2025)

	Ref	Expression
Assertion	tposid	$$⊢Xtpos\mathrm{I}Y=⟨Y,X⟩$$

Proof

Step	Hyp	Ref	Expression
1		ovtpos	$$⊢Xtpos\mathrm{I}Y=Y\mathrm{I}X$$
2		df-ov	$$⊢Y\mathrm{I}X=\mathrm{I}\left(⟨Y,X⟩\right)$$
3		opex	$$⊢⟨Y,X⟩\in \mathrm{V}$$
4		fvi	$$⊢⟨Y,X⟩\in \mathrm{V}\to \mathrm{I}\left(⟨Y,X⟩\right)=⟨Y,X⟩$$
5	3 4	ax-mp	$$⊢\mathrm{I}\left(⟨Y,X⟩\right)=⟨Y,X⟩$$
6	1 2 5	3eqtri	$$⊢Xtpos\mathrm{I}Y=⟨Y,X⟩$$