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Mirrors > Home > ILE Home > Th. List > nfn | GIF version |
Description: Inference associated with nfnt 1656. (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 1656 | . 2 ⊢ (Ⅎ𝑥𝜑 → Ⅎ𝑥 ¬ 𝜑) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Ⅎ𝑥 ¬ 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 Ⅎwnf 1460 |
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 614 ax-in2 615 ax-5 1447 ax-gen 1449 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 |
This theorem is referenced by: nfdc 1659 19.32dc 1679 nfnae 1722 mo2n 2054 nfne 2440 nfnel 2449 nfdif 3258 nfpo 4303 0neqopab 5923 nfsup 6994 ismkvnex 7156 mkvprop 7159 zsupcllemstep 11949 oddpwdclemndvds 12174 ismkvnnlem 14941 |
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