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Mirrors > Home > ILE Home > Th. List > nff | Unicode version |
Description: Bound-variable hypothesis builder for a mapping. (Contributed by NM, 29-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nff.1 | |
nff.2 | |
nff.3 |
Ref | Expression |
---|---|
nff |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f 4926 | . 2 | |
2 | nff.1 | . . . 4 | |
3 | nff.2 | . . . 4 | |
4 | 2, 3 | nffn 5015 | . . 3 |
5 | 2 | nfrn 4597 | . . . 4 |
6 | nff.3 | . . . 4 | |
7 | 5, 6 | nfss 2992 | . . 3 |
8 | 4, 7 | nfan 1497 | . 2 |
9 | 1, 8 | nfxfr 1403 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wnf 1389 wnfc 2206 wss 2973 crn 4364 wfn 4917 wf 4918 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-br 3786 df-opab 3840 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-fun 4924 df-fn 4925 df-f 4926 |
This theorem is referenced by: nff1 5110 |
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