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Theorem bnj1397 29268
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1397.1  |-  ( ph  ->  E. x ps )
bnj1397.2  |-  ( ps 
->  A. x ps )
Assertion
Ref Expression
bnj1397  |-  ( ph  ->  ps )

Proof of Theorem bnj1397
StepHypRef Expression
1 bnj1397.1 . 2  |-  ( ph  ->  E. x ps )
2 bnj1397.2 . . 3  |-  ( ps 
->  A. x ps )
3219.9h 1795 . 2  |-  ( E. x ps  <->  ps )
41, 3sylib 190 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550   E.wex 1551
This theorem is referenced by:  bnj981  29383  bnj1398  29465  bnj1408  29467  bnj1450  29481  bnj1501  29498
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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