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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 ((φψ) ↔ (¬ φ ψ))

Proof of Theorem imor
StepHypRef Expression
1 notnot 282 . . 3 (φ ↔ ¬ ¬ φ)
21imbi1i 315 . 2 ((φψ) ↔ (¬ ¬ φψ))
3 df-or 359 . 2 ((¬ φ ψ) ↔ (¬ ¬ φψ))
42, 3bitr4i 243 1 ((φψ) ↔ (¬ φ ψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357 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 177  df-or 359 This theorem is referenced by:  imori  402  imorri  403  pm4.62  408  pm4.52  477  pm4.78  565  rb-bijust  1514  rb-imdf  1515  rb-ax1  1517  nf4  1868  r19.30  2756  dfimak2  4298  nncaddccl  4419  nndisjeq  4429  preaddccan2lem1  4454  ltfintrilem1  4465  evenoddnnnul  4514  leconnnc  6218  addccan2nclem2  6264  nchoicelem16  6304
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