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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 1492 | . 2 ⊢ (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑) | |
2 | nex.1 | . 2 ⊢ ¬ 𝜑 | |
3 | 1, 2 | mpgbi 1445 | 1 ⊢ ¬ ∃𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∃wex 1485 |
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 609 ax-in2 610 ax-5 1440 ax-gen 1442 ax-ie2 1487 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 |
This theorem is referenced by: ru 2954 0nelxp 4639 0xp 4691 dm0 4825 co02 5124 0fv 5531 mpo0 5923 0npr 7445 0g0 12630 |
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