Theorem cbvalivw 1674

Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of [KalishMontague] p. 86. (Contributed by NM, 9-Apr-2017.)

Hypothesis

Ref	Expression
cbvalivw.1	|- (x = y -> (ph -> ps))

Assertion

Ref	Expression
cbvalivw	|- (A.xph -> A.yps)

Distinct variable groups:   x,y   ps,x   ph,y

Allowed substitution hints:   ph(x)   ps(y)

Proof of Theorem cbvalivw

Step	Hyp	Ref	Expression
1		cbvalivw.1	. . 3 |- (x = y -> (ph -> ps))
2	1	spimvw 1669	. 2 |- (A.xph -> ps)
3	2	alrimiv 1631	1 |- (A.xph -> A.yps)

Syntax hints:   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  cbvalvw  1702  alcomiw  1704  ax10lem1  1936