Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1095 Structured version   Unicode version

Theorem bnj1095 29214
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 2757 . 2  |-  ( A. x  e.  A  ps  ->  A. x A. x  e.  A  ps )
31, 2hbxfrbi 1578 1  |-  ( ph  ->  A. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   A.wal 1550   A.wral 2707
This theorem is referenced by:  bnj1379  29264  bnj605  29340  bnj594  29345  bnj607  29349  bnj911  29365  bnj964  29376  bnj983  29384  bnj1093  29411  bnj1123  29417  bnj1145  29424  bnj1417  29472
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-ral 2712
  Copyright terms: Public domain W3C validator