Theorem cbvopabvOLD

Description: Obsolete version of cbvopabv as of 15-Oct-2024. (Contributed by NM, 15-Oct-1996) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvopabvOLD.1	$$⊢\left(x=z\wedge y=w\right)\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	cbvopabvOLD	$$⊢\left\{⟨x,y⟩|\phi \right\}=\left\{⟨z,w⟩|\psi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		cbvopabvOLD.1	$$⊢\left(x=z\wedge y=w\right)\to \left(\phi \leftrightarrow \psi \right)$$
2		nfv	$$⊢Ⅎz\phi$$
3		nfv	$$⊢Ⅎw\phi$$
4		nfv	$$⊢Ⅎx\psi$$
5		nfv	$$⊢Ⅎy\psi$$
6	2 3 4 5 1	cbvopab	$$⊢\left\{⟨x,y⟩|\phi \right\}=\left\{⟨z,w⟩|\psi \right\}$$