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Theorem bnj1196 29143
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1196.1  |-  ( ph  ->  E. x  e.  A  ps )
Assertion
Ref Expression
bnj1196  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )

Proof of Theorem bnj1196
StepHypRef Expression
1 bnj1196.1 . 2  |-  ( ph  ->  E. x  e.  A  ps )
2 df-rex 2562 . 2  |-  ( E. x  e.  A  ps  <->  E. x ( x  e.  A  /\  ps )
)
31, 2sylib 188 1  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wex 1531    e. wcel 1696   E.wrex 2557
This theorem is referenced by:  bnj1209  29145  bnj1265  29161  bnj1379  29179  bnj1521  29199  bnj900  29277  bnj986  29302  bnj1189  29355  bnj1245  29360  bnj1286  29365  bnj1311  29370  bnj1450  29396  bnj1498  29407
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-rex 2562
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