Theorem cbvalivw 1934

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. x ph -> A. y ps )

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 1927	. 2 |- ( A. x ph -> ps )
3	2	alrimiv 1855	1 |- ( A. x ph -> A. y ps )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  alcomiw  1971  cbvaev  1979  axc11next  38607