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Theorem bnj1196 29167
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 2712 . 2  |-  ( E. x  e.  A  ps  <->  E. x ( x  e.  A  /\  ps )
)
31, 2sylib 190 1  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   E.wex 1551    e. wcel 1726   E.wrex 2707
This theorem is referenced by:  bnj1209  29169  bnj1265  29185  bnj1379  29203  bnj1521  29223  bnj900  29301  bnj986  29326  bnj1189  29379  bnj1245  29384  bnj1286  29389  bnj1311  29394  bnj1450  29420  bnj1498  29431
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 179  df-rex 2712
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