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Theorem cbvalivw 1642
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
StepHypRef Expression
1 cbvalivw.1 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
21spimvw 1639 . 2  |-  ( A. x ph  ->  ps )
32alrimiv 1617 1  |-  ( A. x ph  ->  A. y ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  cbvalvw  1676  alcomiw  1678  ax10lem1  1876
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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