Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj133 Unicode version

Theorem bnj133 28810
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj133.1  |-  ( ph  <->  E. x ps )
bnj133.2  |-  ( ch  <->  ps )
Assertion
Ref Expression
bnj133  |-  ( ph  <->  E. x ch )

Proof of Theorem bnj133
StepHypRef Expression
1 bnj133.1 . 2  |-  ( ph  <->  E. x ps )
2 bnj133.2 . . 3  |-  ( ch  <->  ps )
32exbii 1589 . 2  |-  ( E. x ch  <->  E. x ps )
41, 3bitr4i 244 1  |-  ( ph  <->  E. x ch )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   E.wex 1547
This theorem is referenced by:  bnj150  28965  bnj983  29040  bnj984  29041  bnj985  29042  bnj1090  29066  bnj1514  29150
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563
This theorem depends on definitions:  df-bi 178  df-ex 1548
  Copyright terms: Public domain W3C validator