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Mirrors > Home > ILE Home > Th. List > pm2.51 | GIF version |
Description: Theorem *2.51 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm2.51 | ⊢ (¬ (𝜑 → 𝜓) → (𝜑 → ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 5 | . . 3 ⊢ (𝜓 → (𝜑 → 𝜓)) | |
2 | 1 | con3i 594 | . 2 ⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓) |
3 | 2 | a1d 22 | 1 ⊢ (¬ (𝜑 → 𝜓) → (𝜑 → ¬ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-in1 576 ax-in2 577 |
This theorem is referenced by: (None) |
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