Theorem cbvopab1v

Description: Rule used to change the first bound variable in an ordered pair abstraction, using implicit substitution. (Contributed by NM, 31-Jul-2003) (Proof shortened by Eric Schmidt, 4-Apr-2007)

	Ref	Expression
Hypothesis	cbvopab1v.1	|- ( x = z -> ( ph <-> ps ) )
Assertion	cbvopab1v	|- { <. x , y >. | ph } = { <. z , y >. | ps }

Proof

Step	Hyp	Ref	Expression
1		cbvopab1v.1	|- ( x = z -> ( ph <-> ps ) )
2		nfv	|- F/ z ph
3		nfv	|- F/ x ps
4	2 3 1	cbvopab1	|- { <. x , y >. | ph } = { <. z , y >. | ps }