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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oeq1 5364 |
. . 3
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2 | fveq1 5428 |
. . . . . 6
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3 | fveq1 5428 |
. . . . . 6
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4 | 2, 3 | breq12d 3950 |
. . . . 5
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5 | 4 | bibi2d 231 |
. . . 4
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6 | 5 | 2ralbidv 2462 |
. . 3
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7 | 1, 6 | anbi12d 465 |
. 2
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8 | df-isom 5140 |
. 2
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9 | df-isom 5140 |
. 2
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10 | 7, 8, 9 | 3bitr4g 222 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 df-fv 5139 df-isom 5140 |
This theorem is referenced by: isores1 5723 ordiso 6929 infrenegsupex 9416 zfz1isolem1 10615 zfz1iso 10616 infxrnegsupex 11064 relogiso 13002 |
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