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Theorem bnj1299 28851
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 28838 . 2  |-  ( E. x  e.  A  ( ps  /\  ch )  ->  E. x  e.  A  ps )
31, 2syl 15 1  |-  ( ph  ->  E. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E.wrex 2544
This theorem is referenced by:  bnj1497  29090  bnj1498  29091  bnj1501  29097
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-ral 2548  df-rex 2549
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