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Theorem dral2-o 2231
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 2020 using ax-10o 2189. (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 2203 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
2 dral2-o.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2albidh 1597 1  |-  ( A. x  x  =  y  ->  ( A. z ph  <->  A. z ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546
This theorem is referenced by:  ax11eq  2243  ax11el  2244  ax11indalem  2247  ax11inda2ALT  2248
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-7 1745  ax-4 2185  ax-5o 2186  ax-6o 2187  ax-10o 2189  ax-12o 2192
This theorem depends on definitions:  df-bi 178  df-ex 1548
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