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Theorem dral2-o 32426
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). Version of dral2 2122 using ax-c11 32384. (Contributed by NM, 27-Feb-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dral2-o.1  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
Assertion
Ref Expression
dral2-o  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )

Proof of Theorem dral2-o
StepHypRef Expression
1 hbae-o 32398 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
2 dral2-o.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2albidh 1721 1  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188   A.wal 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-11 1893  ax-c5 32380  ax-c4 32381  ax-c7 32382  ax-c11 32384  ax-c9 32387
This theorem depends on definitions:  df-bi 189  df-ex 1661
This theorem is referenced by:  ax12eq  32437  ax12el  32438  ax12indalem  32441  ax12inda2ALT  32442
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