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Theorem 19.45 1814
Description: Theorem 19.45 of [Margaris] p. 90. (Contributed by NM, 5-Aug-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 1592 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.45.1 . . . 4  |-  F/ x ph
3219.9 1783 . . 3  |-  ( E. x ph  <->  ph )
43orbi1i 506 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( ph  \/  E. x ps )
)
51, 4bitri 240 1  |-  ( E. x ( ph  \/  ps )  <->  ( ph  \/  E. x ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357   E.wex 1528   F/wnf 1531
This theorem is referenced by:  eeor  1826
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-or 359  df-an 360  df-ex 1529  df-nf 1532
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