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Mirrors > Home > ILE Home > Th. List > nfnd | GIF version |
Description: Deduction associated with nfnt 1667. (Contributed by Mario Carneiro, 24-Sep-2016.) |
Ref | Expression |
---|---|
nfnd.1 | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Ref | Expression |
---|---|
nfnd | ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnd.1 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜓) | |
2 | nfnt 1667 | . 2 ⊢ (Ⅎ𝑥𝜓 → Ⅎ𝑥 ¬ 𝜓) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → Ⅎ𝑥 ¬ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 Ⅎwnf 1471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1458 ax-gen 1460 ax-ie2 1505 ax-4 1521 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 |
This theorem is referenced by: nfned 2454 nfneld 2463 nfifd 3576 |
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