Theorem cbvaliw

Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of KalishMontague p. 86. (Contributed by NM, 19-Apr-2017)

	Ref	Expression
Hypotheses	cbvaliw.1	|- ( A. x ph -> A. y A. x ph )
	cbvaliw.2	|- ( -. ps -> A. x -. ps )
	cbvaliw.3	|- ( x = y -> ( ph -> ps ) )
Assertion	cbvaliw	|- ( A. x ph -> A. y ps )

Proof

Step	Hyp	Ref	Expression
1		cbvaliw.1	|- ( A. x ph -> A. y A. x ph )
2		cbvaliw.2	|- ( -. ps -> A. x -. ps )
3		cbvaliw.3	|- ( x = y -> ( ph -> ps ) )
4	2 3	spimw	|- ( A. x ph -> ps )
5	1 4	alrimih	|- ( A. x ph -> A. y ps )