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Mirrors > Home > ILE Home > Th. List > nfiso | Unicode version |
Description: Bound-variable hypothesis builder for an isomorphism. (Contributed by NM, 17-May-2004.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
nfiso.1 | |
nfiso.2 | |
nfiso.3 | |
nfiso.4 | |
nfiso.5 |
Ref | Expression |
---|---|
nfiso |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-isom 5132 | . 2 | |
2 | nfiso.1 | . . . 4 | |
3 | nfiso.4 | . . . 4 | |
4 | nfiso.5 | . . . 4 | |
5 | 2, 3, 4 | nff1o 5365 | . . 3 |
6 | nfcv 2281 | . . . . . . 7 | |
7 | nfiso.2 | . . . . . . 7 | |
8 | nfcv 2281 | . . . . . . 7 | |
9 | 6, 7, 8 | nfbr 3974 | . . . . . 6 |
10 | 2, 6 | nffv 5431 | . . . . . . 7 |
11 | nfiso.3 | . . . . . . 7 | |
12 | 2, 8 | nffv 5431 | . . . . . . 7 |
13 | 10, 11, 12 | nfbr 3974 | . . . . . 6 |
14 | 9, 13 | nfbi 1568 | . . . . 5 |
15 | 3, 14 | nfralxy 2471 | . . . 4 |
16 | 3, 15 | nfralxy 2471 | . . 3 |
17 | 5, 16 | nfan 1544 | . 2 |
18 | 1, 17 | nfxfr 1450 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wnf 1436 wnfc 2268 wral 2416 class class class wbr 3929 wf1o 5122 cfv 5123 wiso 5124 |
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 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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-isom 5132 |
This theorem is referenced by: (None) |
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