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Mirrors > Home > MPE Home > Th. List > pm4.8 | Structured version Visualization version GIF version |
Description: Theorem *4.8 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.8 | ⊢ ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.01 179 | . 2 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑) | |
2 | ax-1 6 | . 2 ⊢ (¬ 𝜑 → (𝜑 → ¬ 𝜑)) | |
3 | 1, 2 | impbii 198 | 1 ⊢ ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 195 |
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 196 |
This theorem is referenced by: wl-nannot 32478 ifpimimb 36868 |
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