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Theorem bnj1131 29158
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 1794 . 2  |-  ( E. x ph  <->  ph )
41, 3mpbi 200 1  |-  ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   E.wex 1550
This theorem is referenced by:  bnj1468  29217  bnj1014  29331  bnj1128  29359
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
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