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Theorem equs3 1625
Description: Lemma used in proofs of substitution properties. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equs3  |-  ( E. x ( x  =  y  /\  ph )  <->  -. 
A. x ( x  =  y  ->  -.  ph ) )

Proof of Theorem equs3
StepHypRef Expression
1 alinexa 1565 . 2  |-  ( A. x ( x  =  y  ->  -.  ph )  <->  -. 
E. x ( x  =  y  /\  ph ) )
21con2bii 322 1  |-  ( E. x ( x  =  y  /\  ph )  <->  -. 
A. x ( x  =  y  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358   A.wal 1527   E.wex 1528
This theorem is referenced by:  equs5e  1829  sbn  2002
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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