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Theorem a16gbNEW7 29522
Description: A generalization of axiom ax-16 2096. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a16gbNEW7  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem a16gbNEW7
StepHypRef Expression
1 a16gNEW7 29521 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
2 sp 1728 . 2  |-  ( A. z ph  ->  ph )
31, 2impbid1 194 1  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530
This theorem is referenced by:  sbalNEW7  29588
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  ax-8 1661  ax-6 1715  ax-11 1727  ax-12 1878  ax-7v 29419
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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