Theorem cbvrex

Description: Rule used to change bound variables, using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvrexw when possible. (Contributed by NM, 31-Jul-2003) (Proof shortened by Andrew Salmon, 8-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	cbvral.1	|- F/ y ph
	cbvral.2	|- F/ x ps
	cbvral.3	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbvrex	|- ( E. x e. A ph <-> E. y e. A ps )

Proof

Step	Hyp	Ref	Expression
1		cbvral.1	|- F/ y ph
2		cbvral.2	|- F/ x ps
3		cbvral.3	|- ( x = y -> ( ph <-> ps ) )
4		nfcv	|- F/_ x A
5		nfcv	|- F/_ y A
6	4 5 1 2 3	cbvrexf	|- ( E. x e. A ph <-> E. y e. A ps )