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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 6284 | . 2 recs | |
2 | nfcv 2312 | . . . . 5 | |
3 | nfv 1521 | . . . . . 6 | |
4 | nfcv 2312 | . . . . . . 7 | |
5 | nfrecs.f | . . . . . . . . 9 | |
6 | nfcv 2312 | . . . . . . . . 9 | |
7 | 5, 6 | nffv 5506 | . . . . . . . 8 |
8 | 7 | nfeq2 2324 | . . . . . . 7 |
9 | 4, 8 | nfralxy 2508 | . . . . . 6 |
10 | 3, 9 | nfan 1558 | . . . . 5 |
11 | 2, 10 | nfrexxy 2509 | . . . 4 |
12 | 11 | nfab 2317 | . . 3 |
13 | 12 | nfuni 3802 | . 2 |
14 | 1, 13 | nfcxfr 2309 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 cab 2156 wnfc 2299 wral 2448 wrex 2449 cuni 3796 con0 4348 cres 4613 wfn 5193 cfv 5198 recscrecs 6283 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-iota 5160 df-fv 5206 df-recs 6284 |
This theorem is referenced by: nffrec 6375 |
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