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Theorem 19.42 1820
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 1819 . 2  |-  ( E. x ( ps  /\  ph )  <->  ( E. x ps  /\  ph ) )
3 exancom 1578 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
4 ancom 439 . 2  |-  ( (
ph  /\  E. x ps )  <->  ( E. x ps  /\  ph ) )
52, 3, 43bitr4i 270 1  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   E.wex 1533   F/wnf 1536
This theorem is referenced by:  19.42v  1857  eean  1864  r2exf  2580  bnj596  28042  bnj916  28232  bnj983  28250
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-11 1719
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1534  df-nf 1537
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