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Theorem imor 412
Description: Implication in terms of disjunction. Theorem *4.6 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-1993.)
Assertion
Ref Expression
imor  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )

Proof of Theorem imor
StepHypRef Expression
1 notnot 291 . . 3  |-  ( ph  <->  -. 
-.  ph )
21imbi1i 325 . 2  |-  ( (
ph  ->  ps )  <->  ( -.  -.  ph  ->  ps )
)
3 df-or 370 . 2  |-  ( ( -.  ph  \/  ps ) 
<->  ( -.  -.  ph  ->  ps ) )
42, 3bitr4i 252 1  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ wo 368
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 185  df-or 370
This theorem is referenced by:  imori  413  imorri  414  pm4.62  419  pm4.52  491  pm4.78  582  rb-bijust  1566  rb-imdf  1567  rb-ax1  1569  nf4  1911  r19.30  3006  soxp  6896  modom  7720  dffin7-2  8777  algcvgblem  14064  divgcdodd  14118  chrelat2i  26976  disjex  27140  disjexc  27141  meran1  29469  meran3  29471  itg2addnclem2  29660  dvasin  29696  impor  30097  biimpor  30100  stoweidlem14  31330  alimp-surprise  32285  eximp-surprise  32289  hbimpgVD  32793  bj-dfbi5  33231  bj-dfif3  33236  bj-dfif4  33237  bj-dfif7  33241  bj-andnotim  33267  bj-nf2  33288  hlrelat2  34208
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