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Theorem orcanai 875
Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994.)
Hypothesis
Ref Expression
orcanai.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
orcanai ((𝜑 ∧ ¬ 𝜓) → 𝜒)

Proof of Theorem orcanai
StepHypRef Expression
1 orcanai.1 . . 3 (𝜑 → (𝜓𝜒))
21ord 678 . 2 (𝜑 → (¬ 𝜓𝜒))
32imp 122 1 ((𝜑 ∧ ¬ 𝜓) → 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102  wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 580  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  fsumsplit  10801
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