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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 | pm2.21 612 | . 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓)) | |
3 | 1, 2 | jaod 712 | 1 ⊢ (¬ 𝜑 → ((𝜓 ∨ 𝜑) → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 703 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 610 ax-io 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: biorfi 741 pm2.64 796 stdcn 842 pm5.71dc 956 ecased 1344 19.30dc 1620 dveeq2 1808 prel12 3756 funun 5240 |
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