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Mirrors > Home > ILE Home > Th. List > nffo | Unicode version |
Description: Bound-variable hypothesis builder for an onto function. (Contributed by NM, 16-May-2004.) |
Ref | Expression |
---|---|
nffo.1 | |
nffo.2 | |
nffo.3 |
Ref | Expression |
---|---|
nffo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fo 4908 | . 2 | |
2 | nffo.1 | . . . 4 | |
3 | nffo.2 | . . . 4 | |
4 | 2, 3 | nffn 4995 | . . 3 |
5 | 2 | nfrn 4579 | . . . 4 |
6 | nffo.3 | . . . 4 | |
7 | 5, 6 | nfeq 2185 | . . 3 |
8 | 4, 7 | nfan 1457 | . 2 |
9 | 1, 8 | nfxfr 1363 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wceq 1243 wnf 1349 wnfc 2165 crn 4346 wfn 4897 wfo 4900 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-fun 4904 df-fn 4905 df-fo 4908 |
This theorem is referenced by: nff1o 5124 |
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