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Mirrors > Home > ILE Home > Th. List > mtand | GIF version |
Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.) |
Ref | Expression |
---|---|
mtand.1 | ⊢ (𝜑 → ¬ 𝜒) |
mtand.2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
mtand | ⊢ (𝜑 → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtand.1 | . 2 ⊢ (𝜑 → ¬ 𝜒) | |
2 | mtand.2 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
3 | 2 | ex 114 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
4 | 1, 3 | mtod 635 | 1 ⊢ (𝜑 → ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 107 ax-in1 586 ax-in2 587 |
This theorem is referenced by: frirrg 4230 phpm 6709 diffisn 6737 tridc 6743 pm54.43 6992 addcanprleml 7363 addcanprlemu 7364 iseqf1olemklt 10144 pw2dvdseulemle 11683 sqne2sq 11693 ctinfomlemom 11778 pwle2 12872 nninfalllemn 12879 |
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