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Theorem bnj1238 29155
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1238.1  |-  ( ph  <->  E. x  e.  A  ( ps  /\  ch )
)
Assertion
Ref Expression
bnj1238  |-  ( ph  ->  E. x  e.  A  ps )

Proof of Theorem bnj1238
StepHypRef Expression
1 bnj1238.1 . 2  |-  ( ph  <->  E. x  e.  A  ( ps  /\  ch )
)
2 bnj1239 29154 . 2  |-  ( E. x  e.  A  ( ps  /\  ch )  ->  E. x  e.  A  ps )
31, 2sylbi 187 1  |-  ( ph  ->  E. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358   E.wrex 2557
This theorem is referenced by:  bnj1245  29360  bnj1256  29361  bnj1259  29362  bnj1311  29370  bnj1371  29375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-ral 2561  df-rex 2562
  Copyright terms: Public domain W3C validator