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Mirrors > Home > MPE Home > Th. List > pm4.81 | Structured version Visualization version GIF version |
Description: Theorem *4.81 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.81 | ⊢ ((¬ 𝜑 → 𝜑) ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.18 122 | . 2 ⊢ ((¬ 𝜑 → 𝜑) → 𝜑) | |
2 | pm2.24 121 | . 2 ⊢ (𝜑 → (¬ 𝜑 → 𝜑)) | |
3 | 1, 2 | impbii 199 | 1 ⊢ ((¬ 𝜑 → 𝜑) ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 196 |
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 197 |
This theorem is referenced by: ifpimimb 37849 ifpimim 37854 |
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