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Theorem equs3 1697
Description: Lemma used in proofs of substitution properties. (Contributed by NM, 10-May-1993.)
Assertion
Ref Expression
equs3  |-  ( E. x ( x  =  y  /\  ph )  <->  -. 
A. x ( x  =  y  ->  -.  ph ) )

Proof of Theorem equs3
StepHypRef Expression
1 alinexa 1631 . 2  |-  ( A. x ( x  =  y  ->  -.  ph )  <->  -. 
E. x ( x  =  y  /\  ph ) )
21con2bii 332 1  |-  ( E. x ( x  =  y  /\  ph )  <->  -. 
A. x ( x  =  y  ->  -.  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    /\ wa 369   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588
This theorem is referenced by:  sbnOLD  2090
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