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Theorem bnj1196 34273
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 2810 . 2  |-  ( E. x  e.  A  ps  <->  E. x ( x  e.  A  /\  ps )
)
31, 2sylib 196 1  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   E.wex 1617    e. wcel 1823   E.wrex 2805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-rex 2810
This theorem is referenced by:  bnj1209  34275  bnj1265  34291  bnj1379  34309  bnj1521  34329  bnj900  34407  bnj986  34432  bnj1189  34485  bnj1245  34490  bnj1286  34495  bnj1311  34500  bnj1450  34526  bnj1498  34537
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