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| Mirrors > Home > ILE Home > Th. List > nfn | GIF version | ||
| Description: Inference associated with nfnt 1678. (Contributed by Mario Carneiro, 11-Aug-2016.) |
| Ref | Expression |
|---|---|
| nfn.1 | ⊢ Ⅎ𝑥𝜑 |
| Ref | Expression |
|---|---|
| nfn | ⊢ Ⅎ𝑥 ¬ 𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfn.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
| 2 | nfnt 1678 | . 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ Ⅎ𝑥 ¬ 𝜑 |
| Colors of variables: wff set class |
| Syntax hints: ¬ wn 3 Ⅎwnf 1482 |
| 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 1469 ax-gen 1471 ax-ie2 1516 ax-4 1532 ax-ial 1556 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-fal 1378 df-nf 1483 |
| This theorem is referenced by: nfdc 1681 19.32dc 1701 nfnae 1744 mo2n 2081 nfne 2468 nfnel 2477 nfdif 3293 nfpo 4346 0neqopab 5980 nfsup 7076 ismkvnex 7239 mkvprop 7242 zsupcllemstep 10353 oddpwdclemndvds 12412 ismkvnnlem 15855 |
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