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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 2665 | . . . . 5 | |
2 | 1 | imbi1d 230 | . . . 4 |
3 | 2 | raleqbi1dv 2673 | . . 3 |
4 | sseq1 3170 | . . 3 | |
5 | 3, 4 | imbi12d 233 | . 2 |
6 | df-frfor 4316 | . 2 FrFor | |
7 | df-frfor 4316 | . 2 FrFor | |
8 | 5, 6, 7 | 3bitr4g 222 | 1 FrFor FrFor |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1348 wcel 2141 wral 2448 wss 3121 class class class wbr 3989 FrFor wfrfor 4312 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-in 3127 df-ss 3134 df-frfor 4316 |
This theorem is referenced by: freq2 4331 |
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