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Mirrors > Home > ILE Home > Th. List > frforeq2 | Unicode version |
Description: Equality theorem for the well-founded predicate. (Contributed by Jim Kingdon, 22-Sep-2021.) |
Ref | Expression |
---|---|
frforeq2 | FrFor FrFor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq 2505 | . . . . 5 | |
2 | 1 | imbi1d 220 | . . . 4 |
3 | 2 | raleqbi1dv 2513 | . . 3 |
4 | sseq1 2966 | . . 3 | |
5 | 3, 4 | imbi12d 223 | . 2 |
6 | df-frfor 4068 | . 2 FrFor | |
7 | df-frfor 4068 | . 2 FrFor | |
8 | 5, 6, 7 | 3bitr4g 212 | 1 FrFor FrFor |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 wral 2306 wss 2917 class class class wbr 3764 FrFor wfrfor 4064 |
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-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-in 2924 df-ss 2931 df-frfor 4068 |
This theorem is referenced by: freq2 4083 |
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