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Mirrors > Home > ILE Home > Th. List > nfn | GIF version |
Description: Inference associated with nfnt 1619. (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 1619 | . 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Ⅎ𝑥 ¬ 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 Ⅎwnf 1421 |
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 588 ax-in2 589 ax-5 1408 ax-gen 1410 ax-ie2 1455 ax-4 1472 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 |
This theorem is referenced by: nfdc 1622 19.32dc 1642 nfnae 1685 mo2n 2005 nfne 2378 nfnel 2387 nfdif 3167 nfpo 4193 0neqopab 5784 nfsup 6847 ismkvnex 6997 mkvprop 7000 zsupcllemstep 11565 oddpwdclemndvds 11776 |
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