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Theorem 19.44 1887
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 1612 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.44.1 . . . 4  |-  F/ x ps
3219.9 1791 . . 3  |-  ( E. x ps  <->  ps )
43orbi2i 506 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( E. x ph  \/  ps )
)
51, 4bitri 241 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358   E.wex 1547   F/wnf 1550
This theorem is referenced by:  eeor  1896  grothprim  8642  eeorOLD7  29015
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-ex 1548  df-nf 1551
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