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Mirrors > Home > ILE Home > Th. List > pm2.32 | GIF version |
Description: Theorem *2.32 of [WhiteheadRussell] p. 105. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.32 | ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ (𝜓 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orass 762 | . 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒))) | |
2 | 1 | biimpi 119 | 1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ (𝜓 ∨ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 703 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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