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Mirrors > Home > ILE Home > Th. List > supeq2 | Unicode version |
Description: Equality theorem for supremum. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
supeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeq 2722 | . . . 4 | |
2 | raleq 2665 | . . . . . 6 | |
3 | 2 | anbi2d 461 | . . . . 5 |
4 | 3 | rabbidv 2719 | . . . 4 |
5 | 1, 4 | eqtrd 2203 | . . 3 |
6 | 5 | unieqd 3805 | . 2 |
7 | df-sup 6957 | . 2 | |
8 | df-sup 6957 | . 2 | |
9 | 6, 7, 8 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1348 wral 2448 wrex 2449 crab 2452 cuni 3794 class class class wbr 3987 csup 6955 |
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-rex 2454 df-rab 2457 df-uni 3795 df-sup 6957 |
This theorem is referenced by: infeq2 6987 |
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