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Mirrors > Home > ILE Home > Th. List > unissi | GIF version |
Description: Subclass relationship for subclass union. Inference form of uniss 3674. (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 3674 | . 2 ⊢ (𝐴 ⊆ 𝐵 → ∪ 𝐴 ⊆ ∪ 𝐵) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ∪ 𝐴 ⊆ ∪ 𝐵 |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 2999 ∪ cuni 3653 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-in 3005 df-ss 3012 df-uni 3654 |
This theorem is referenced by: unidif 3685 unixpss 4551 tfrcllemssrecs 6117 |
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