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Mirrors > Home > MPE Home > Th. List > pm2.54 | Structured version Visualization version GIF version |
Description: Theorem *2.54 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.54 | ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-or 848 | . 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓)) | |
2 | 1 | biimpri 231 | 1 ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → 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-or 848 |
This theorem is referenced by: orrd 863 orim12dALT 912 tsbi3 36030 |
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