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Mirrors > Home > NFE Home > Th. List > mt4 | GIF version |
Description: The rule of modus tollens. (Contributed by Wolf Lammen, 12-May-2013.) |
Ref | Expression |
---|---|
mt4.1 | ⊢ φ |
mt4.2 | ⊢ (¬ ψ → ¬ φ) |
Ref | Expression |
---|---|
mt4 | ⊢ ψ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mt4.1 | . 2 ⊢ φ | |
2 | mt4.2 | . . 3 ⊢ (¬ ψ → ¬ φ) | |
3 | 2 | con4i 122 | . 2 ⊢ (φ → ψ) |
4 | 1, 3 | ax-mp 8 | 1 ⊢ 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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