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Mirrors > Home > ILE Home > Th. List > orcanai | GIF version |
Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994.) |
Ref | Expression |
---|---|
orcanai.1 | ⊢ (𝜑 → (𝜓 ∨ 𝜒)) |
Ref | Expression |
---|---|
orcanai | ⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcanai.1 | . . 3 ⊢ (𝜑 → (𝜓 ∨ 𝜒)) | |
2 | 1 | ord 724 | . 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
3 | 2 | imp 124 | 1 ⊢ ((𝜑 ∧ ¬ 𝜓) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 104 ∨ wo 708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: fsumsplit 11408 pcgcd 12320 lgsdir2 14305 |
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