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Mirrors > Home > ILE Home > Th. List > isoeq4 | Unicode version |
Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.) |
Ref | Expression |
---|---|
isoeq4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oeq2 5118 | . . 3 | |
2 | raleq 2505 | . . . 4 | |
3 | 2 | raleqbi1dv 2513 | . . 3 |
4 | 1, 3 | anbi12d 442 | . 2 |
5 | df-isom 4911 | . 2 | |
6 | df-isom 4911 | . 2 | |
7 | 4, 5, 6 | 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-tru 1246 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 df-isom 4911 |
This theorem is referenced by: (None) |
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