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Mirrors > Home > NFE Home > Th. List > pm2.52 | GIF version |
Description: Theorem *2.52 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 8-Oct-2012.) |
Ref | Expression |
---|---|
pm2.52 | ⊢ (¬ (φ → ψ) → (¬ φ → ¬ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.521 146 | . 2 ⊢ (¬ (φ → ψ) → (ψ → φ)) | |
2 | 1 | con3d 125 | 1 ⊢ (¬ (φ → ψ) → (¬ φ → ¬ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem is referenced by: (None) |
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