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Mirrors > Home > ILE Home > Th. List > nexdv | GIF version |
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
nexdv.1 | ⊢ (𝜑 → ¬ 𝜓) |
Ref | Expression |
---|---|
nexdv | ⊢ (𝜑 → ¬ ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1506 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | nexdv.1 | . 2 ⊢ (𝜑 → ¬ 𝜓) | |
3 | 1, 2 | nexd 1593 | 1 ⊢ (𝜑 → ¬ ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∃wex 1472 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1427 ax-gen 1429 ax-ie2 1474 ax-17 1506 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 |
This theorem is referenced by: pw1nct 13575 |
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