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Mirrors > Home > ILE Home > Th. List > soeq1 | Unicode version |
Description: Equality theorem for the strict ordering predicate. (Contributed by NM, 16-Mar-1997.) |
Ref | Expression |
---|---|
soeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | poeq1 4036 | . . 3 | |
2 | breq 3766 | . . . . . 6 | |
3 | breq 3766 | . . . . . . 7 | |
4 | breq 3766 | . . . . . . 7 | |
5 | 3, 4 | orbi12d 707 | . . . . . 6 |
6 | 2, 5 | imbi12d 223 | . . . . 5 |
7 | 6 | 2ralbidv 2348 | . . . 4 |
8 | 7 | ralbidv 2326 | . . 3 |
9 | 1, 8 | anbi12d 442 | . 2 |
10 | df-iso 4034 | . 2 | |
11 | df-iso 4034 | . 2 | |
12 | 9, 10, 11 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wo 629 wceq 1243 wral 2306 class class class wbr 3764 wpo 4031 wor 4032 |
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-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 df-ral 2311 df-br 3765 df-po 4033 df-iso 4034 |
This theorem is referenced by: (None) |
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