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Mirrors > Home > ILE Home > Th. List > isoeq1 | Unicode version |
Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.) |
Ref | Expression |
---|---|
isoeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oeq1 5351 | . . 3 | |
2 | fveq1 5413 | . . . . . 6 | |
3 | fveq1 5413 | . . . . . 6 | |
4 | 2, 3 | breq12d 3937 | . . . . 5 |
5 | 4 | bibi2d 231 | . . . 4 |
6 | 5 | 2ralbidv 2457 | . . 3 |
7 | 1, 6 | anbi12d 464 | . 2 |
8 | df-isom 5127 | . 2 | |
9 | df-isom 5127 | . 2 | |
10 | 7, 8, 9 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wral 2414 class class class wbr 3924 wf1o 5117 cfv 5118 wiso 5119 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-iota 5083 df-fun 5120 df-fn 5121 df-f 5122 df-f1 5123 df-fo 5124 df-f1o 5125 df-fv 5126 df-isom 5127 |
This theorem is referenced by: isores1 5708 ordiso 6914 infrenegsupex 9382 zfz1isolem1 10576 zfz1iso 10577 infxrnegsupex 11025 |
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