Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 3239 | . 2 ⊢ 𝐴 ⊆ (𝐴 ∪ 𝐵) | |
2 | uncom 3220 | . 2 ⊢ (𝐴 ∪ 𝐵) = (𝐵 ∪ 𝐴) | |
3 | 1, 2 | sseqtri 3131 | 1 ⊢ 𝐴 ⊆ (𝐵 ∪ 𝐴) |
Colors of variables: wff set class |
Syntax hints: ∪ cun 3069 ⊆ wss 3071 |
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-un 3075 df-in 3077 df-ss 3084 |
This theorem is referenced by: ssun4 3242 elun2 3244 unv 3400 un00 3409 snsspr2 3669 snsstp3 3672 unexb 4363 rnexg 4804 brtpos0 6149 ac6sfi 6792 caserel 6972 pnfxr 7818 ltrelxr 7825 un0mulcl 9011 fsumsplit 11176 bdunexb 13118 |
Copyright terms: Public domain | W3C validator |