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Theorem bnj132 29165
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj132.1  |-  ( ph  <->  E. x ( ps  ->  ch ) )
Assertion
Ref Expression
bnj132  |-  ( ph  <->  ( ps  ->  E. x ch ) )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x)    ch( x)

Proof of Theorem bnj132
StepHypRef Expression
1 bnj132.1 . 2  |-  ( ph  <->  E. x ( ps  ->  ch ) )
2 19.37v 1923 . 2  |-  ( E. x ( ps  ->  ch )  <->  ( ps  ->  E. x ch ) )
31, 2bitri 242 1  |-  ( ph  <->  ( ps  ->  E. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   E.wex 1551
This theorem is referenced by:  bnj996  29400
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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