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Theorem 19.44 1899
Description: Theorem 19.44 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
19.44.1  |-  F/ x ps
Assertion
Ref Expression
19.44  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  ps ) )

Proof of Theorem 19.44
StepHypRef Expression
1 19.43 1616 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.44.1 . . . 4  |-  F/ x ps
3219.9 1798 . . 3  |-  ( E. x ps  <->  ps )
43orbi2i 507 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( E. x ph  \/  ps )
)
51, 4bitri 242 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359   E.wex 1551   F/wnf 1554
This theorem is referenced by:  eeor  1908  grothprim  8714  eeorOLD7  29773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-ex 1552  df-nf 1555
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