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Mirrors > Home > ILE Home > Th. List > nffrec | Unicode version |
Description: Bound-variable hypothesis builder for the finite recursive definition generator. (Contributed by Jim Kingdon, 30-May-2020.) |
Ref | Expression |
---|---|
nffrec.1 | |
nffrec.2 |
Ref | Expression |
---|---|
nffrec | frec |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-frec 5978 | . 2 frec recs | |
2 | nfcv 2178 | . . . . 5 | |
3 | nfcv 2178 | . . . . . . . 8 | |
4 | nfv 1421 | . . . . . . . . 9 | |
5 | nffrec.1 | . . . . . . . . . . 11 | |
6 | nfcv 2178 | . . . . . . . . . . 11 | |
7 | 5, 6 | nffv 5185 | . . . . . . . . . 10 |
8 | 7 | nfcri 2172 | . . . . . . . . 9 |
9 | 4, 8 | nfan 1457 | . . . . . . . 8 |
10 | 3, 9 | nfrexya 2363 | . . . . . . 7 |
11 | nfv 1421 | . . . . . . . 8 | |
12 | nffrec.2 | . . . . . . . . 9 | |
13 | 12 | nfcri 2172 | . . . . . . . 8 |
14 | 11, 13 | nfan 1457 | . . . . . . 7 |
15 | 10, 14 | nfor 1466 | . . . . . 6 |
16 | 15 | nfab 2182 | . . . . 5 |
17 | 2, 16 | nfmpt 3849 | . . . 4 |
18 | 17 | nfrecs 5922 | . . 3 recs |
19 | 18, 3 | nfres 4614 | . 2 recs |
20 | 1, 19 | nfcxfr 2175 | 1 frec |
Colors of variables: wff set class |
Syntax hints: wa 97 wo 629 wceq 1243 wcel 1393 cab 2026 wnfc 2165 wrex 2307 cvv 2557 c0 3224 cmpt 3818 csuc 4102 com 4313 cdm 4345 cres 4347 cfv 4902 recscrecs 5919 freccfrec 5977 |
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-rex 2312 df-rab 2315 df-v 2559 df-un 2922 df-in 2924 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-xp 4351 df-res 4357 df-iota 4867 df-fv 4910 df-recs 5920 df-frec 5978 |
This theorem is referenced by: nfiseq 9218 |
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