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Theorem bnj946 29122
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj946.1  |-  ( ph  <->  A. x  e.  A  ps )
Assertion
Ref Expression
bnj946  |-  ( ph  <->  A. x ( x  e.  A  ->  ps )
)

Proof of Theorem bnj946
StepHypRef Expression
1 bnj946.1 . 2  |-  ( ph  <->  A. x  e.  A  ps )
2 df-ral 2561 . 2  |-  ( A. x  e.  A  ps  <->  A. x ( x  e.  A  ->  ps )
)
31, 2bitri 240 1  |-  ( ph  <->  A. x ( x  e.  A  ->  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530    e. wcel 1696   A.wral 2556
This theorem is referenced by:  bnj1379  29179  bnj570  29253  bnj571  29254
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-ral 2561
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