Theorem cbvalvw

Description: Change bound variable. Uses only Tarski's FOL axiom schemes. See cbvalv for a version with fewer disjoint variable conditions but requiring more axioms. (Contributed by NM, 9-Apr-2017) (Proof shortened by Wolf Lammen, 28-Feb-2018)

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

Proof

Step	Hyp	Ref	Expression
1		cbvalvw.1	|- ( x = y -> ( ph <-> ps ) )
2		ax-5	|- ( A. x ph -> A. y A. x ph )
3		ax-5	|- ( -. ps -> A. x -. ps )
4		ax-5	|- ( A. y ps -> A. x A. y ps )
5		ax-5	|- ( -. ph -> A. y -. ph )
6	2 3 4 5 1	cbvalw	|- ( A. x ph <-> A. y ps )