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Theorem bnj1095 29129
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1095.1  |-  ( ph  <->  A. x  e.  A  ps )
Assertion
Ref Expression
bnj1095  |-  ( ph  ->  A. x ph )

Proof of Theorem bnj1095
StepHypRef Expression
1 bnj1095.1 . 2  |-  ( ph  <->  A. x  e.  A  ps )
2 hbra1 2605 . 2  |-  ( A. x  e.  A  ps  ->  A. x A. x  e.  A  ps )
31, 2hbxfrbi 1558 1  |-  ( ph  ->  A. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530   A.wral 2556
This theorem is referenced by:  bnj1379  29179  bnj605  29255  bnj594  29260  bnj607  29264  bnj911  29280  bnj964  29291  bnj983  29299  bnj1093  29326  bnj1123  29332  bnj1145  29339  bnj1417  29387
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-ral 2561
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