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Mirrors > Home > ILE Home > Th. List > unissi | GIF version |
Description: Subclass relationship for subclass union. Inference form of uniss 3757. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
unissi.1 | ⊢ 𝐴 ⊆ 𝐵 |
Ref | Expression |
---|---|
unissi | ⊢ ∪ 𝐴 ⊆ ∪ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unissi.1 | . 2 ⊢ 𝐴 ⊆ 𝐵 | |
2 | uniss 3757 | . 2 ⊢ (𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∪ 𝐴 ⊆ ∪ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3071 ∪ cuni 3736 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 |
This theorem is referenced by: unidif 3768 unixpss 4652 tfrcllemssrecs 6249 tgvalex 12219 tgval2 12220 eltg4i 12224 ntrss2 12290 isopn3 12294 |
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