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Mirrors > Home > ILE Home > Th. List > nex | GIF version |
Description: Generalization rule for negated wff. (Contributed by NM, 18-May-1994.) |
Ref | Expression |
---|---|
nex.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
nex | ⊢ ¬ ∃𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex 1429 | . 2 ⊢ (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑) | |
2 | nex.1 | . 2 ⊢ ¬ 𝜑 | |
3 | 1, 2 | mpgbi 1382 | 1 ⊢ ¬ ∃𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∃wex 1422 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-5 1377 ax-gen 1379 ax-ie2 1424 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-fal 1291 |
This theorem is referenced by: ru 2825 0nelxp 4428 0xp 4476 dm0 4608 co02 4898 0fv 5284 mpt20 5653 0npr 6945 |
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