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Mirrors > Home > MPE Home > Th. List > pm2.8 | Structured version Visualization version GIF version |
Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.) |
Ref | Expression |
---|---|
pm2.8 | ⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.53 850 | . . 3 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓)) | |
2 | 1 | con1d 147 | . 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜓 → 𝜑)) |
3 | 2 | orim1d 965 | 1 ⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 846 |
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-an 400 df-or 847 |
This theorem is referenced by: (None) |
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