Theorem cbvoprab3v

Description: Rule used to change the third bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 8-Oct-2004) (Revised by David Abernethy, 19-Jun-2012)

	Ref	Expression
Hypothesis	cbvoprab3v.1	|- ( z = w -> ( ph <-> ps ) )
Assertion	cbvoprab3v	|- { <. <. x , y >. , z >. | ph } = { <. <. x , y >. , w >. | ps }

Proof

Step	Hyp	Ref	Expression
1		cbvoprab3v.1	|- ( z = w -> ( ph <-> ps ) )
2		nfv	|- F/ w ph
3		nfv	|- F/ z ps
4	2 3 1	cbvoprab3	|- { <. <. x , y >. , z >. | ph } = { <. <. x , y >. , w >. | ps }