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Mirrors > Home > MPE Home > Th. List > Mathboxes > 3orel3 | 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 |
---|---|
3orel3 | ⊢ (¬ 𝜒 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3or 1090 | . 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒)) | |
2 | orel2 891 | . 2 ⊢ (¬ 𝜒 → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ 𝜓))) | |
3 | 1, 2 | syl5bi 245 | 1 ⊢ (¬ 𝜒 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 847 ∨ w3o 1088 |
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 210 df-or 848 df-3or 1090 |
This theorem is referenced by: 3orel13 33372 ttrcltr 33512 nolesgn2o 33608 nosep2o 33619 noinfbnd1lem5 33664 noinfbnd2lem1 33667 |
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