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Theorem pm4.83 937
Description: Theorem *4.83 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.83  |-  ( ( ( ph  ->  ps )  /\  ( -.  ph  ->  ps ) )  <->  ps )

Proof of Theorem pm4.83
StepHypRef Expression
1 exmid 416 . . 3  |-  ( ph  \/  -.  ph )
21a1bi 338 . 2  |-  ( ps  <->  ( ( ph  \/  -.  ph )  ->  ps )
)
3 jaob 790 . 2  |-  ( ( ( ph  \/  -.  ph )  ->  ps )  <->  ( ( ph  ->  ps )  /\  ( -.  ph  ->  ps ) ) )
42, 3bitr2i 253 1  |-  ( ( ( ph  ->  ps )  /\  ( -.  ph  ->  ps ) )  <->  ps )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    \/ wo 369    /\ wa 370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372
This theorem is referenced by:  dmdbr5ati  27907  cvlsupr3  32619  rp-fakeanorass  35860
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