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Theorem 19.42h 1622
Description: Theorem 19.42 of [Margaris] p. 90. New proofs should use 19.42 1623 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 1620 . 2  |-  ( E. x ( ps  /\  ph )  <->  ( E. x ps  /\  ph ) )
3 exancom 1544 . 2  |-  ( E. x ( ph  /\  ps )  <->  E. x ( ps 
/\  ph ) )
4 ancom 262 . 2  |-  ( (
ph  /\  E. x ps )  <->  ( E. x ps  /\  ph ) )
52, 3, 43bitr4i 210 1  |-  ( E. x ( ph  /\  ps )  <->  ( ph  /\  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103   A.wal 1287   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.42v  1834
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