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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 2652 | . . . . 5 | |
2 | 1 | imbi1d 230 | . . . 4 |
3 | 2 | raleqbi1dv 2660 | . . 3 |
4 | sseq1 3151 | . . 3 | |
5 | 3, 4 | imbi12d 233 | . 2 |
6 | df-frfor 4291 | . 2 FrFor | |
7 | df-frfor 4291 | . 2 FrFor | |
8 | 5, 6, 7 | 3bitr4g 222 | 1 FrFor FrFor |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wcel 2128 wral 2435 wss 3102 class class class wbr 3965 FrFor wfrfor 4287 |
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-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-in 3108 df-ss 3115 df-frfor 4291 |
This theorem is referenced by: freq2 4306 |
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