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Theorem dral2-o 2120
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 1906 using ax-10o 2078. (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 2092 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
2 dral2-o.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2albidh 1577 1  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527
This theorem is referenced by:  ax11eq  2132  ax11el  2133  ax11indalem  2136  ax11inda2ALT  2137
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-7 1708  ax-4 2074  ax-5o 2075  ax-6o 2076  ax-10o 2078  ax-12o 2081
This theorem depends on definitions:  df-bi 177
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