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Mirrors > Home > ILE Home > Th. List > isorel | Unicode version |
Description: An isomorphism connects binary relations via its function values. (Contributed by NM, 27-Apr-2004.) |
Ref | Expression |
---|---|
isorel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-isom 5102 | . . 3 | |
2 | 1 | simprbi 273 | . 2 |
3 | breq1 3902 | . . . 4 | |
4 | fveq2 5389 | . . . . 5 | |
5 | 4 | breq1d 3909 | . . . 4 |
6 | 3, 5 | bibi12d 234 | . . 3 |
7 | breq2 3903 | . . . 4 | |
8 | fveq2 5389 | . . . . 5 | |
9 | 8 | breq2d 3911 | . . . 4 |
10 | 7, 9 | bibi12d 234 | . . 3 |
11 | 6, 10 | rspc2v 2776 | . 2 |
12 | 2, 11 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wcel 1465 wral 2393 class class class wbr 3899 wf1o 5092 cfv 5093 wiso 5094 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-isom 5102 |
This theorem is referenced by: isoresbr 5678 isoini 5687 isopolem 5691 isosolem 5693 smoiso 6167 isotilem 6861 supisolem 6863 ordiso2 6888 leisorel 10548 zfz1isolemiso 10550 seq3coll 10553 |
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