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Mirrors > Home > ILE Home > Th. List > djueq1 | Unicode version |
Description: Equality theorem for disjoint union. (Contributed by Jim Kingdon, 23-Jun-2022.) |
Ref | Expression |
---|---|
djueq1 | ⊔ ⊔ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2137 | . 2 | |
2 | djueq12 6917 | . 2 ⊔ ⊔ | |
3 | 1, 2 | mpan2 421 | 1 ⊔ ⊔ |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 ⊔ cdju 6915 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-opab 3985 df-xp 4540 df-dju 6916 |
This theorem is referenced by: enumct 6993 ctssexmid 7017 unct 11943 subctctexmid 13185 sbthom 13210 |
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