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Theorem a16gb 1990
Description: A generalization of axiom ax-16 2083. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
a16gb  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem a16gb
StepHypRef Expression
1 a16g 1885 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
2 sp 1716 . 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 1527
This theorem is referenced by:  sbal  2066
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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