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Theorem equsalh 2139
Description: An equivalence related to implicit substitution. (Contributed by NM, 2-Jun-1993.)
Hypotheses
Ref Expression
equsalh.1  |-  ( ps 
->  A. x ps )
equsalh.2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
equsalh  |-  ( A. x ( x  =  y  ->  ph )  <->  ps )

Proof of Theorem equsalh
StepHypRef Expression
1 equsalh.1 . . 3  |-  ( ps 
->  A. x ps )
21nfi 1684 . 2  |-  F/ x ps
3 equsalh.2 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
42, 3equsal 2138 1  |-  ( A. x ( x  =  y  ->  ph )  <->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943  ax-13 2101
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674  df-nf 1678
This theorem is referenced by:  dvelimf-o  32544
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