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Theorem ax16gb 1877
Description: A generalization of axiom ax-c16 2201. (Contributed by NM, 15-May-1993.)
Assertion
Ref Expression
ax16gb  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem ax16gb
StepHypRef Expression
1 axc16g 1875 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
2 sp 1796 . 2  |-  ( A. z ph  ->  ph )
31, 2impbid1 203 1  |-  ( A. x  x  =  y  ->  ( ph  <->  A. z ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  sbal  2181  sbalOLD  2182
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