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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 3979 | . . . . . . 7 | |
2 | 1 | imbi1d 230 | . . . . . 6 |
3 | 2 | ralbidv 2464 | . . . . 5 |
4 | 3 | imbi1d 230 | . . . 4 |
5 | 4 | ralbidv 2464 | . . 3 |
6 | 5 | imbi1d 230 | . 2 |
7 | df-frfor 4304 | . 2 FrFor | |
8 | df-frfor 4304 | . 2 FrFor | |
9 | 6, 7, 8 | 3bitr4g 222 | 1 FrFor FrFor |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 wcel 2135 wral 2442 wss 3112 class class class wbr 3977 FrFor wfrfor 4300 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-cleq 2157 df-clel 2160 df-ral 2447 df-br 3978 df-frfor 4304 |
This theorem is referenced by: freq1 4317 |
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