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Mirrors > Home > ILE Home > Th. List > frforeq1 | Unicode version |
Description: Equality theorem for the well-founded predicate. (Contributed by Jim Kingdon, 22-Sep-2021.) |
Ref | Expression |
---|---|
frforeq1 | FrFor FrFor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 3787 | . . . . . . 7 | |
2 | 1 | imbi1d 229 | . . . . . 6 |
3 | 2 | ralbidv 2368 | . . . . 5 |
4 | 3 | imbi1d 229 | . . . 4 |
5 | 4 | ralbidv 2368 | . . 3 |
6 | 5 | imbi1d 229 | . 2 |
7 | df-frfor 4086 | . 2 FrFor | |
8 | df-frfor 4086 | . 2 FrFor | |
9 | 6, 7, 8 | 3bitr4g 221 | 1 FrFor FrFor |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wcel 1433 wral 2348 wss 2973 class class class wbr 3785 FrFor wfrfor 4082 |
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-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-frfor 4086 |
This theorem is referenced by: freq1 4099 |
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