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Theorem dral2-o 1858
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 1857 using ax-10o 1835. (Contributed by NM, 27-Feb-2005.)
Hypothesis
Ref Expression
dral1.1  |-  ( 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 1841 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
2 dral1.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2albidh 1589 1  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1532
This theorem is referenced by:  ax11eq  2105  ax11el  2106  ax11indalem  2110  ax11inda2ALT  2111
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-12o 1664  ax-9 1684  ax-4 1692  ax-10o 1835
This theorem depends on definitions:  df-bi 179  df-nf 1540
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