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Mirrors > Home > ILE Home > Th. List > nfn | GIF version |
Description: Inference associated with nfnt 1592. (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 1592 | . 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ Ⅎ𝑥 ¬ 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 Ⅎwnf 1395 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-5 1382 ax-gen 1384 ax-ie2 1429 ax-4 1446 ax-ial 1473 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-fal 1296 df-nf 1396 |
This theorem is referenced by: nfdc 1595 19.32dc 1615 nfnae 1658 mo2n 1977 nfne 2349 nfnel 2358 nfdif 3122 nfpo 4137 0neqopab 5708 nfsup 6741 zsupcllemstep 11280 oddpwdclemndvds 11488 |
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