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Theorem bnj1198 29144
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1198.1  |-  ( ph  ->  E. x ps )
bnj1198.2  |-  ( ps'  <->  ps )
Assertion
Ref Expression
bnj1198  |-  ( ph  ->  E. x ps' )

Proof of Theorem bnj1198
StepHypRef Expression
1 bnj1198.1 . 2  |-  ( ph  ->  E. x ps )
2 bnj1198.2 . . 3  |-  ( ps'  <->  ps )
32exbii 1572 . 2  |-  ( E. x ps'  <->  E. x ps )
41, 3sylibr 203 1  |-  ( ph  ->  E. x ps' )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   E.wex 1531
This theorem is referenced by:  bnj1209  29145  bnj1275  29162  bnj1340  29172  bnj1345  29173  bnj605  29255  bnj607  29264  bnj906  29278  bnj908  29279  bnj1189  29355  bnj1450  29396  bnj1312  29404
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-ex 1532
  Copyright terms: Public domain W3C validator