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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 1419 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | nexdv.1 | . 2 ⊢ (𝜑 → ¬ 𝜓) | |
3 | 1, 2 | nexd 1504 | 1 ⊢ (𝜑 → ¬ ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∃wex 1381 |
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 ax-5 1336 ax-gen 1338 ax-ie2 1383 ax-17 1419 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 |
This theorem is referenced by: (None) |
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