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Mirrors > Home > MPE Home > Th. List > isoeq1 | Structured version Visualization version 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 5818 |
. . 3
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2 | fveq1 5878 |
. . . . . 6
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3 | fveq1 5878 |
. . . . . 6
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4 | 2, 3 | breq12d 4408 |
. . . . 5
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5 | 4 | bibi2d 325 |
. . . 4
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6 | 5 | 2ralbidv 2832 |
. . 3
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7 | 1, 6 | anbi12d 725 |
. 2
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8 | df-isom 5598 |
. 2
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9 | df-isom 5598 |
. 2
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10 | 7, 8, 9 | 3bitr4g 296 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-isom 5598 |
This theorem is referenced by: isores1 6243 wemoiso 6797 wemoiso2 6798 ordiso 8049 oieu 8072 finnisoeu 8562 iunfictbso 8563 infrenegsup 10613 infmsupOLD 10614 ltweuz 12213 fz1isolem 12665 isercolllem2 13806 isercoll 13808 dvgt0lem2 23034 efcvx 23483 relogiso 23626 logccv 23687 erdszelem1 29986 erdsze 29997 erdsze2lem2 29999 fzisoeu 37606 fourierdlem36 38118 fourierdlem96 38178 fourierdlem97 38179 fourierdlem98 38180 fourierdlem99 38181 fourierdlem105 38187 fourierdlem106 38188 fourierdlem108 38190 fourierdlem110 38192 fourierdlem112 38194 fourierdlem113 38195 fourierdlem115 38197 |
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