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Mirrors > Home > MPE Home > Th. List > pm2.36 | Structured version Visualization version GIF version |
Description: Theorem *2.36 of [WhiteheadRussell] p. 105. (Contributed by NM, 6-Mar-2008.) |
Ref | Expression |
---|---|
pm2.36 | ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜒 ∨ 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm1.4 869 | . 2 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) | |
2 | pm2.38 969 | . 2 ⊢ ((𝜓 → 𝜒) → ((𝜓 ∨ 𝜑) → (𝜒 ∨ 𝜑))) | |
3 | 1, 2 | syl5 34 | 1 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜒 ∨ 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 847 |
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 848 |
This theorem is referenced by: (None) |
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