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Mirrors > Home > ILE Home > Th. List > orel1 | GIF version |
Description: Elimination of disjunction by denial of a disjunct. Theorem *2.55 of [WhiteheadRussell] p. 107. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Wolf Lammen, 21-Jul-2012.) |
Ref | Expression |
---|---|
orel1 | ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓) → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.53 641 | . 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓)) | |
2 | 1 | com12 27 | 1 ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓) → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: biorf 663 pm2.25dc 792 pm2.85dc 811 euor2 1958 prel12 3542 funun 4944 acexmidlema 5503 acexmidlemb 5504 |
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