Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 5117 | . . 3 | |
2 | fveq1 5177 | . . . . . 6 | |
3 | fveq1 5177 | . . . . . 6 | |
4 | 2, 3 | breq12d 3777 | . . . . 5 |
5 | 4 | bibi2d 221 | . . . 4 |
6 | 5 | 2ralbidv 2348 | . . 3 |
7 | 1, 6 | anbi12d 442 | . 2 |
8 | df-isom 4911 | . 2 | |
9 | df-isom 4911 | . 2 | |
10 | 7, 8, 9 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wral 2306 class class class wbr 3764 wf1o 4901 cfv 4902 wiso 4903 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 df-fv 4910 df-isom 4911 |
This theorem is referenced by: isores1 5454 ordiso 6358 |
Copyright terms: Public domain | W3C validator |