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Theorem 19.42 1816
Description: Theorem 19.42 of [Margaris] p. 90. (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 1815 . 2  |-  ( E. x ( ps  /\  ph )  <->  ( E. x ps  /\  ph ) )
3 exancom 1573 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
4 ancom 437 . 2  |-  ( (
ph  /\  E. x ps )  <->  ( E. x ps  /\  ph ) )
52, 3, 43bitr4i 268 1  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1528   F/wnf 1531
This theorem is referenced by:  19.42v  1846  eean  1853  r2exf  2579  bnj596  28775  bnj916  28965  bnj983  28983
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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