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Theorem bnj1095 32130
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 2811 . 2  |-  ( A. x  e.  A  ps  ->  A. x A. x  e.  A  ps )
31, 2hbxfrbi 1614 1  |-  ( ph  ->  A. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368   A.wral 2799
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  df-ral 2804
This theorem is referenced by:  bnj1379  32179  bnj605  32255  bnj594  32260  bnj607  32264  bnj911  32280  bnj964  32291  bnj983  32299  bnj1093  32326  bnj1123  32332  bnj1145  32339  bnj1417  32387
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