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Theorem bnj133 29029
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 1592 . 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 1550
This theorem is referenced by:  bnj150  29184  bnj983  29259  bnj984  29260  bnj985  29261  bnj1090  29285  bnj1514  29369
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-ex 1551
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