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Mirrors > Home > ILE Home > Th. List > djueq12 | Unicode version |
Description: Equality theorem for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022.) |
Ref | Expression |
---|---|
djueq12 | ⊔ ⊔ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpeq2 4624 | . . . 4 | |
2 | 1 | adantr 274 | . . 3 |
3 | xpeq2 4624 | . . . 4 | |
4 | 3 | adantl 275 | . . 3 |
5 | 2, 4 | uneq12d 3282 | . 2 |
6 | df-dju 7013 | . 2 ⊔ | |
7 | df-dju 7013 | . 2 ⊔ | |
8 | 5, 6, 7 | 3eqtr4g 2228 | 1 ⊔ ⊔ |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 cun 3119 c0 3414 csn 3581 cxp 4607 c1o 6386 ⊔ cdju 7012 |
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-v 2732 df-un 3125 df-opab 4049 df-xp 4615 df-dju 7013 |
This theorem is referenced by: djueq1 7015 djueq2 7016 casef 7063 |
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