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Mirrors > Home > ILE Home > Th. List > inegd | GIF version |
Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017.) |
Ref | Expression |
---|---|
inegd.1 | ⊢ ((𝜑 ∧ 𝜓) → ⊥) |
Ref | Expression |
---|---|
inegd | ⊢ (𝜑 → ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inegd.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → ⊥) | |
2 | 1 | ex 108 | . 2 ⊢ (𝜑 → (𝜓 → ⊥)) |
3 | dfnot 1262 | . 2 ⊢ (¬ 𝜓 ↔ (𝜓 → ⊥)) | |
4 | 2, 3 | sylibr 137 | 1 ⊢ (𝜑 → ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 97 ⊥wfal 1248 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 |
This theorem is referenced by: genpdisj 6621 cauappcvgprlemdisj 6749 caucvgprlemdisj 6772 caucvgprprlemdisj 6800 resqrexlemgt0 9618 resqrexlemoverl 9619 leabs 9672 climge0 9845 |
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