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Mirrors > Home > ILE Home > Th. List > nfrecs | Unicode version |
Description: Bound-variable hypothesis builder for recs. (Contributed by Stefan O'Rear, 18-Jan-2015.) |
Ref | Expression |
---|---|
nfrecs.f |
Ref | Expression |
---|---|
nfrecs | recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-recs 6202 | . 2 recs | |
2 | nfcv 2281 | . . . . 5 | |
3 | nfv 1508 | . . . . . 6 | |
4 | nfcv 2281 | . . . . . . 7 | |
5 | nfrecs.f | . . . . . . . . 9 | |
6 | nfcv 2281 | . . . . . . . . 9 | |
7 | 5, 6 | nffv 5431 | . . . . . . . 8 |
8 | 7 | nfeq2 2293 | . . . . . . 7 |
9 | 4, 8 | nfralxy 2471 | . . . . . 6 |
10 | 3, 9 | nfan 1544 | . . . . 5 |
11 | 2, 10 | nfrexxy 2472 | . . . 4 |
12 | 11 | nfab 2286 | . . 3 |
13 | 12 | nfuni 3742 | . 2 |
14 | 1, 13 | nfcxfr 2278 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 cab 2125 wnfc 2268 wral 2416 wrex 2417 cuni 3736 con0 4285 cres 4541 wfn 5118 cfv 5123 recscrecs 6201 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-recs 6202 |
This theorem is referenced by: nffrec 6293 |
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