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Mirrors > Home > ILE Home > Th. List > nfpo | Unicode version |
Description: Bound-variable hypothesis builder for partial orders. (Contributed by Stefan O'Rear, 20-Jan-2015.) |
Ref | Expression |
---|---|
nfpo.r | |
nfpo.a |
Ref | Expression |
---|---|
nfpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-po 4279 | . 2 | |
2 | nfpo.a | . . 3 | |
3 | nfcv 2312 | . . . . . . . 8 | |
4 | nfpo.r | . . . . . . . 8 | |
5 | 3, 4, 3 | nfbr 4033 | . . . . . . 7 |
6 | 5 | nfn 1651 | . . . . . 6 |
7 | nfcv 2312 | . . . . . . . . 9 | |
8 | 3, 4, 7 | nfbr 4033 | . . . . . . . 8 |
9 | nfcv 2312 | . . . . . . . . 9 | |
10 | 7, 4, 9 | nfbr 4033 | . . . . . . . 8 |
11 | 8, 10 | nfan 1558 | . . . . . . 7 |
12 | 3, 4, 9 | nfbr 4033 | . . . . . . 7 |
13 | 11, 12 | nfim 1565 | . . . . . 6 |
14 | 6, 13 | nfan 1558 | . . . . 5 |
15 | 2, 14 | nfralxy 2508 | . . . 4 |
16 | 2, 15 | nfralxy 2508 | . . 3 |
17 | 2, 16 | nfralxy 2508 | . 2 |
18 | 1, 17 | nfxfr 1467 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wnf 1453 wnfc 2299 wral 2448 class class class wbr 3987 wpo 4277 |
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 609 ax-in2 610 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-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-po 4279 |
This theorem is referenced by: nfso 4285 |
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