Theorem cbvopabv

Description: Rule used to change bound variables in an ordered-pair class abstraction, using implicit substitution. (Contributed by NM, 15-Oct-1996)

	Ref	Expression
Hypothesis	cbvopabv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
Assertion	cbvopabv	|- { <. x , y >. | ph } = { <. z , w >. | ps }

Proof

Step	Hyp	Ref	Expression
1		cbvopabv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
2		nfv	|- F/ z ph
3		nfv	|- F/ w ph
4		nfv	|- F/ x ps
5		nfv	|- F/ y ps
6	2 3 4 5 1	cbvopab	|- { <. x , y >. | ph } = { <. z , w >. | ps }