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Mirrors > Home > ILE Home > Th. List > orim2 | GIF version |
Description: Axiom *1.6 (Sum) of [WhiteheadRussell] p. 97. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
orim2 | ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜒)) | |
2 | 1 | orim2d 702 | 1 ⊢ ((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: pm2.76 721 pm2.81 724 |
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