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Theorem imor 403
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 284 . . 3  |-  ( ph  <->  -. 
-.  ph )
21imbi1i 317 . 2  |-  ( (
ph  ->  ps )  <->  ( -.  -.  ph  ->  ps )
)
3 df-or 361 . 2  |-  ( ( -.  ph  \/  ps ) 
<->  ( -.  -.  ph  ->  ps ) )
42, 3bitr4i 245 1  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    \/ wo 359
This theorem is referenced by:  imori  404  imorri  405  pm4.62  410  pm4.52  479  pm4.78  568  jcabOLD  839  rb-bijust  1509  rb-imdf  1510  rb-ax1  1512  nf4  1780  r19.30  2656  soxp  6127  modom  6996  dffin7-2  7957  algcvgblem  12674  divgcdodd  12725  chrelat2i  22870  meran1  24190  meran3  24192  clsbldimp  24419  stoweidlem14  27063  hbimpgVD  27693  hlrelat2  28722
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361
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