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Theorem bnj1131 29135
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 . . . 4  |-  ( ph  ->  A. x ph )
32nfi 1541 . . 3  |-  F/ x ph
4319.9 1795 . 2  |-  ( E. x ph  <->  ph )
51, 4mpbi 199 1  |-  ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531
This theorem is referenced by:  bnj1468  29194  bnj1014  29308  bnj1128  29336
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-ex 1532  df-nf 1535
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