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Theorem 19.45 1644
Description: Theorem 19.45 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)
Hypothesis
Ref Expression
19.45.1  |-  F/ x ph
Assertion
Ref Expression
19.45  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )

Proof of Theorem 19.45
StepHypRef Expression
1 19.43 1590 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.45.1 . . . 4  |-  F/ x ph
3219.9 1606 . . 3  |-  ( E. x ph  <->  ph )
43orbi1i 735 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( ph  \/  E. x ps )
)
51, 4bitri 183 1  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 680   F/wnf 1419   E.wex 1451
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  eeor  1656
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