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Theorem imor 401
Description: Implication in terms of disjunction. Theorem *4.6 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
imor  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )

Proof of Theorem imor
StepHypRef Expression
1 notnot 282 . . 3  |-  ( ph  <->  -. 
-.  ph )
21imbi1i 315 . 2  |-  ( (
ph  ->  ps )  <->  ( -.  -.  ph  ->  ps )
)
3 df-or 359 . 2  |-  ( ( -.  ph  \/  ps ) 
<->  ( -.  -.  ph  ->  ps ) )
42, 3bitr4i 243 1  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    \/ wo 357
This theorem is referenced by:  imori  402  imorri  403  pm4.62  408  pm4.52  477  pm4.78  565  rb-bijust  1504  rb-imdf  1505  rb-ax1  1507  nf4  1800  r19.30  2685  soxp  6228  modom  7063  dffin7-2  8024  algcvgblem  12747  divgcdodd  12798  chrelat2i  22945  meran1  24261  meran3  24263  dvreasin  24334  clsbldimp  24500  stoweidlem14  27175  hbimpgVD  28053  hlrelat2  28965
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
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