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Mirrors > Home > ILE Home > Th. List > pm2.76 | GIF version |
Description: Theorem *2.76 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm2.76 | ⊢ ((𝜑 ∨ (𝜓 → 𝜒)) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 633 | . . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒)) | |
2 | 1 | a1d 22 | . 2 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒))) |
3 | orim2 703 | . 2 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒))) | |
4 | 2, 3 | jaoi 636 | 1 ⊢ ((𝜑 ∨ (𝜓 → 𝜒)) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → 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-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm2.75 722 pm2.81 724 orimdidc 812 equs5or 1711 |
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