Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1198 Unicode version

Theorem bnj1198 28201
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 1569 . 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 1528
This theorem is referenced by:  bnj1209  28202  bnj1275  28219  bnj1340  28229  bnj1345  28230  bnj605  28312  bnj607  28321  bnj906  28335  bnj908  28336  bnj1189  28412  bnj1450  28453  bnj1312  28461
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-ex 1529
  Copyright terms: Public domain W3C validator