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Theorem bnj1095 29167
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 2786 . 2  |-  ( A. x  e.  A  ps  ->  A. x A. x  e.  A  ps )
31, 2hbxfrbi 1664 1  |-  ( ph  ->  A. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1403   A.wral 2754
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-12 1878
This theorem depends on definitions:  df-bi 185  df-ex 1634  df-nf 1638  df-ral 2759
This theorem is referenced by:  bnj1379  29216  bnj605  29292  bnj594  29297  bnj607  29301  bnj911  29317  bnj964  29328  bnj983  29336  bnj1093  29363  bnj1123  29369  bnj1145  29376  bnj1417  29424
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