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Theorem bnj1397 28867
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 . . . 4  |-  ( ps 
->  A. x ps )
32nfi 1538 . . 3  |-  F/ x ps
4319.9 1783 . 2  |-  ( E. x ps  <->  ps )
51, 4sylib 188 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  bnj981  28982  bnj1398  29064  bnj1408  29066  bnj1450  29080  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  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-ex 1529  df-nf 1532
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