Theorem cbvralv

Description: Change the bound variable of a restricted universal quantifier using implicit substitution. See cbvralvw based on fewer axioms , but extra disjoint variables. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker cbvralvw when possible. (Contributed by NM, 28-Jan-1997) (New usage is discouraged.)

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