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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 4054 | . . 3 | |
2 | breq 3787 | . . . . . 6 | |
3 | breq 3787 | . . . . . . 7 | |
4 | breq 3787 | . . . . . . 7 | |
5 | 3, 4 | orbi12d 739 | . . . . . 6 |
6 | 2, 5 | imbi12d 232 | . . . . 5 |
7 | 6 | 2ralbidv 2390 | . . . 4 |
8 | 7 | ralbidv 2368 | . . 3 |
9 | 1, 8 | anbi12d 456 | . 2 |
10 | df-iso 4052 | . 2 | |
11 | df-iso 4052 | . 2 | |
12 | 9, 10, 11 | 3bitr4g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wo 661 wceq 1284 wral 2348 class class class wbr 3785 wpo 4049 wor 4050 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-cleq 2074 df-clel 2077 df-ral 2353 df-br 3786 df-po 4051 df-iso 4052 |
This theorem is referenced by: (None) |
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