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Theorem pm5.6 995
Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of [WhiteheadRussell] p. 125. (Contributed by NM, 8-Jun-1994.)
Assertion
Ref Expression
pm5.6 (((𝜑 ∧ ¬ 𝜓) → 𝜒) ↔ (𝜑 → (𝜓𝜒)))

Proof of Theorem pm5.6
StepHypRef Expression
1 impexp 451 . 2 (((𝜑 ∧ ¬ 𝜓) → 𝜒) ↔ (𝜑 → (¬ 𝜓𝜒)))
2 df-or 842 . . 3 ((𝜓𝜒) ↔ (¬ 𝜓𝜒))
32imbi2i 337 . 2 ((𝜑 → (𝜓𝜒)) ↔ (𝜑 → (¬ 𝜓𝜒)))
41, 3bitr4i 279 1 (((𝜑 ∧ ¬ 𝜓) → 𝜒) ↔ (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207  wa 396  wo 841
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 208  df-an 397  df-or 842
This theorem is referenced by:  ssundif  4429  brdom3  9938  grothprim  10244  eliccelico  30426  elicoelioo  30427  ballotlemfc0  31649  ballotlemfcc  31650  elicc3  33562  ifpidg  39735  dfsucon  39767  icccncfext  42046
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