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Mirrors > Home > ILE Home > Th. List > orel2 | GIF version |
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.56 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 5-Apr-2013.) |
Ref | Expression |
---|---|
orel2 | ⊢ (¬ 𝜑 → ((𝜓 ∨ 𝜑) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 21 | . 2 ⊢ (¬ 𝜑 → (𝜓 → 𝜓)) | |
2 | pm2.21 617 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
3 | 1, 2 | jaod 717 | 1 ⊢ (¬ 𝜑 → ((𝜓 ∨ 𝜑) → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ 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: biorfi 746 pm2.64 801 stdcn 847 pm5.71dc 961 ecased 1349 19.30dc 1625 dveeq2 1813 prel12 3767 funun 5252 |
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