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Theorem bnj133 32019
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 1635 . 2  |-  ( E. x ch  <->  E. x ps )
41, 3bitr4i 252 1  |-  ( ph  <->  E. x ch )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  bnj150  32172  bnj983  32247  bnj984  32248  bnj985  32249  bnj1090  32273  bnj1514  32357
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