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Theorem 19.44 1825
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 1595 . 2  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
2 19.44.1 . . . 4  |-  F/ x ps
3219.9 1795 . . 3  |-  ( E. x ps  <->  ps )
43orbi2i 505 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  ( E. x ph  \/  ps )
)
51, 4bitri 240 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357   E.wex 1531   F/wnf 1534
This theorem is referenced by:  eeor  1838  grothprim  8472  eeorOLD7  29653
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1532  df-nf 1535
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