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Mirrors > Home > ILE Home > Th. List > nfsup | Unicode version |
Description: Hypothesis builder for supremum. (Contributed by Mario Carneiro, 20-Mar-2014.) |
Ref | Expression |
---|---|
nfsup.1 | |
nfsup.2 | |
nfsup.3 |
Ref | Expression |
---|---|
nfsup |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sup 6940 | . 2 | |
2 | nfsup.1 | . . . . . 6 | |
3 | nfcv 2306 | . . . . . . . 8 | |
4 | nfsup.3 | . . . . . . . 8 | |
5 | nfcv 2306 | . . . . . . . 8 | |
6 | 3, 4, 5 | nfbr 4022 | . . . . . . 7 |
7 | 6 | nfn 1645 | . . . . . 6 |
8 | 2, 7 | nfralya 2504 | . . . . 5 |
9 | nfsup.2 | . . . . . 6 | |
10 | 5, 4, 3 | nfbr 4022 | . . . . . . 7 |
11 | nfcv 2306 | . . . . . . . . 9 | |
12 | 5, 4, 11 | nfbr 4022 | . . . . . . . 8 |
13 | 2, 12 | nfrexya 2505 | . . . . . . 7 |
14 | 10, 13 | nfim 1559 | . . . . . 6 |
15 | 9, 14 | nfralya 2504 | . . . . 5 |
16 | 8, 15 | nfan 1552 | . . . 4 |
17 | 16, 9 | nfrabxy 2644 | . . 3 |
18 | 17 | nfuni 3789 | . 2 |
19 | 1, 18 | nfcxfr 2303 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wnfc 2293 wral 2442 wrex 2443 crab 2446 cuni 3783 class class class wbr 3976 csup 6938 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-sup 6940 |
This theorem is referenced by: nfinf 6973 infssuzcldc 11869 |
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