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Theorem spimvw 1657
Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)
Hypothesis
Ref Expression
spimvw.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimvw  |-  ( A. x ph  ->  ps )
Distinct variable groups:    x, y    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem spimvw
StepHypRef Expression
1 ax-17 1606 . 2  |-  ( -. 
ps  ->  A. x  -.  ps )
2 spimvw.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spimw 1656 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
This theorem is referenced by:  cbvalivw  1660  spw  1679  alcomiw  1690
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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