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Theorem bnj1131 32098
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1131.1  |-  ( ph  ->  A. x ph )
bnj1131.2  |-  E. x ph
Assertion
Ref Expression
bnj1131  |-  ph

Proof of Theorem bnj1131
StepHypRef Expression
1 bnj1131.2 . 2  |-  E. x ph
2 bnj1131.1 . . 3  |-  ( ph  ->  A. x ph )
3219.9h 1830 . 2  |-  ( E. x ph  <->  ph )
41, 3mpbi 208 1  |-  ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-nf 1591
This theorem is referenced by:  bnj1468  32156  bnj1014  32270  bnj1128  32298
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