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Theorem equsalh 2001
Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-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 1560 . 2  |-  F/ x ps
3 equsalh.2 . 2  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
42, 3equsal 1999 1  |-  ( A. x ( x  =  y  ->  ph )  <->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549
This theorem is referenced by:  dvelimhOLD  2072  dvelimALT  2210  dvelimf-o  2257
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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