Theorem cbvmptvOLD

Description: Obsolete version of cbvmptv as of 17-Nov-2024. (Contributed by Mario Carneiro, 19-Feb-2013) Add disjoint variable condition to avoid ax-13 . See cbvmptvg for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 17-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvmptvOLD.1	$$⊢x=y\to B=C$$
Assertion	cbvmptvOLD	$$⊢\left(x\in A⟼B\right)=\left(y\in A⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		cbvmptvOLD.1	$$⊢x=y\to B=C$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}yB$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}xC$$
4	2 3 1	cbvmpt	$$⊢\left(x\in A⟼B\right)=\left(y\in A⟼C\right)$$