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Theorem 19.42h 1687
Description: Theorem 19.42 of [Margaris] p. 90. New proofs should use 19.42 1688 instead. (Contributed by NM, 18-Aug-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
19.42h.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
19.42h  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )

Proof of Theorem 19.42h
StepHypRef Expression
1 19.42h.1 . . 3  |-  ( ph  ->  A. x ph )
2119.41h 1685 . 2  |-  ( E. x ( ps  /\  ph )  <->  ( E. x ps  /\  ph ) )
3 exancom 1608 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
4 ancom 266 . 2  |-  ( (
ph  /\  E. x ps )  <->  ( E. x ps  /\  ph ) )
52, 3, 43bitr4i 212 1  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105   A.wal 1351   E.wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  19.42v  1906
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