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Theorem 19.42 2071
Description: Theorem 19.42 of [Margaris] p. 90. See 19.42v 1842 for a version requiring fewer axioms. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
19.42.1  |-  F/ x ph
Assertion
Ref Expression
19.42  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )

Proof of Theorem 19.42
StepHypRef Expression
1 19.42.1 . . 3  |-  F/ x ph
2119.41 2070 . 2  |-  ( E. x ( ps  /\  ph )  <->  ( E. x ps  /\  ph ) )
3 exancom 1730 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
4 ancom 457 . 2  |-  ( (
ph  /\  E. x ps )  <->  ( E. x ps  /\  ph ) )
52, 3, 43bitr4i 285 1  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    /\ wa 376   E.wex 1671   F/wnf 1675
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676
This theorem is referenced by:  eean  2092  bnj596  29628  bnj916  29816  bnj983  29834
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