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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > 3orel1 | Structured version Visualization version GIF version |
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.) |
Ref | Expression |
---|---|
3orel1 | ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜓 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3orass 1034 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
2 | orel1 396 | . 2 ⊢ (¬ 𝜑 → ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ 𝜒))) | |
3 | 1, 2 | syl5bi 231 | 1 ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜓 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∨ w3o 1030 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-or 384 df-3or 1032 |
This theorem is referenced by: 3orel2 30847 |
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