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Theorem bnj1397 32849
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 1834 . 2  |-  ( E. x ps  <->  ps )
41, 3sylib 196 1  |-  ( ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1372   E.wex 1591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-12 1798
This theorem depends on definitions:  df-bi 185  df-ex 1592  df-nf 1595
This theorem is referenced by:  bnj981  32964  bnj1398  33046  bnj1408  33048  bnj1450  33062  bnj1501  33079
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