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Mirrors > Home > ILE Home > Th. List > ssun2 | GIF version |
Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
ssun2 | ⊢ 𝐴 ⊆ (𝐵 ∪ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3280 | . 2 ⊢ 𝐴 ⊆ (𝐴 ∪ 𝐵) | |
2 | uncom 3261 | . 2 ⊢ (𝐴 ∪ 𝐵) = (𝐵 ∪ 𝐴) | |
3 | 1, 2 | sseqtri 3171 | 1 ⊢ 𝐴 ⊆ (𝐵 ∪ 𝐴) |
Colors of variables: wff set class |
Syntax hints: ∪ cun 3109 ⊆ wss 3111 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 |
This theorem is referenced by: ssun4 3283 elun2 3285 unv 3441 un00 3450 snsspr2 3716 snsstp3 3719 unexb 4414 rnexg 4863 brtpos0 6211 ac6sfi 6855 caserel 7043 pnfxr 7942 ltrelxr 7950 un0mulcl 9139 fsumsplit 11334 fprodsplitdc 11523 bdunexb 13643 |
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