Theorem cbvrmov

Description: Change the bound variable of a restricted at-most-one quantifier using implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by Alexander van der Vekens, 17-Jun-2017) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvralv.1	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbvrmov	|- ( E* x e. A ph <-> E* y e. A ps )

Proof

Step	Hyp	Ref	Expression
1		cbvralv.1	|- ( x = y -> ( ph <-> ps ) )
2		nfv	|- F/ y ph
3		nfv	|- F/ x ps
4	2 3 1	cbvrmo	|- ( E* x e. A ph <-> E* y e. A ps )