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Theorem bnj1299 29364
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1299.1  |-  ( ph  ->  E. x  e.  A  ( ps  /\  ch )
)
Assertion
Ref Expression
bnj1299  |-  ( ph  ->  E. x  e.  A  ps )

Proof of Theorem bnj1299
StepHypRef Expression
1 bnj1299.1 . 2  |-  ( ph  ->  E. x  e.  A  ( ps  /\  ch )
)
2 bnj1239 29351 . 2  |-  ( E. x  e.  A  ( ps  /\  ch )  ->  E. x  e.  A  ps )
31, 2syl 16 1  |-  ( ph  ->  E. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   E.wrex 2713
This theorem is referenced by:  bnj1497  29603  bnj1498  29604  bnj1501  29610
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-ral 2717  df-rex 2718
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