Theorem ceqsalv

Description: A representation of explicit substitution of a class for a variable, inferred from an implicit substitution hypothesis. (Contributed by NM, 18-Aug-1993)

	Ref	Expression
Hypotheses	ceqsalv.1	|- A e. _V
	ceqsalv.2	|- ( x = A -> ( ph <-> ps ) )
Assertion	ceqsalv	|- ( A. x ( x = A -> ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		ceqsalv.1	|- A e. _V
2		ceqsalv.2	|- ( x = A -> ( ph <-> ps ) )
3		nfv	|- F/ x ps
4	3 1 2	ceqsal	|- ( A. x ( x = A -> ph ) <-> ps )