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Mirrors > Home > ILE Home > Th. List > nfwe | Unicode version |
Description: Bound-variable hypothesis builder for well-orderings. (Contributed by Stefan O'Rear, 20-Jan-2015.) (Revised by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nfwe.r | |
nfwe.a |
Ref | Expression |
---|---|
nfwe |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-wetr 4306 | . 2 | |
2 | nfwe.r | . . . 4 | |
3 | nfwe.a | . . . 4 | |
4 | 2, 3 | nffr 4321 | . . 3 |
5 | nfcv 2306 | . . . . . . . . 9 | |
6 | nfcv 2306 | . . . . . . . . 9 | |
7 | 5, 2, 6 | nfbr 4022 | . . . . . . . 8 |
8 | nfcv 2306 | . . . . . . . . 9 | |
9 | 6, 2, 8 | nfbr 4022 | . . . . . . . 8 |
10 | 7, 9 | nfan 1552 | . . . . . . 7 |
11 | 5, 2, 8 | nfbr 4022 | . . . . . . 7 |
12 | 10, 11 | nfim 1559 | . . . . . 6 |
13 | 3, 12 | nfralxy 2502 | . . . . 5 |
14 | 3, 13 | nfralxy 2502 | . . . 4 |
15 | 3, 14 | nfralxy 2502 | . . 3 |
16 | 4, 15 | nfan 1552 | . 2 |
17 | 1, 16 | nfxfr 1461 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wnf 1447 wnfc 2293 wral 2442 class class class wbr 3976 wfr 4300 wwe 4302 |
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 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-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-frfor 4303 df-frind 4304 df-wetr 4306 |
This theorem is referenced by: (None) |
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