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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 4213 | . 2 | |
2 | nfpo.a | . . 3 | |
3 | nfcv 2279 | . . . . . . . 8 | |
4 | nfpo.r | . . . . . . . 8 | |
5 | 3, 4, 3 | nfbr 3969 | . . . . . . 7 |
6 | 5 | nfn 1636 | . . . . . 6 |
7 | nfcv 2279 | . . . . . . . . 9 | |
8 | 3, 4, 7 | nfbr 3969 | . . . . . . . 8 |
9 | nfcv 2279 | . . . . . . . . 9 | |
10 | 7, 4, 9 | nfbr 3969 | . . . . . . . 8 |
11 | 8, 10 | nfan 1544 | . . . . . . 7 |
12 | 3, 4, 9 | nfbr 3969 | . . . . . . 7 |
13 | 11, 12 | nfim 1551 | . . . . . 6 |
14 | 6, 13 | nfan 1544 | . . . . 5 |
15 | 2, 14 | nfralxy 2469 | . . . 4 |
16 | 2, 15 | nfralxy 2469 | . . 3 |
17 | 2, 16 | nfralxy 2469 | . 2 |
18 | 1, 17 | nfxfr 1450 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wnf 1436 wnfc 2266 wral 2414 class class class wbr 3924 wpo 4211 |
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 603 ax-in2 604 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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-po 4213 |
This theorem is referenced by: nfso 4219 |
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