![]() |
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 3298 | . 2 ⊢ 𝐴 ⊆ (𝐴 ∪ 𝐵) | |
2 | uncom 3279 | . 2 ⊢ (𝐴 ∪ 𝐵) = (𝐵 ∪ 𝐴) | |
3 | 1, 2 | sseqtri 3189 | 1 ⊢ 𝐴 ⊆ (𝐵 ∪ 𝐴) |
Colors of variables: wff set class |
Syntax hints: ∪ cun 3127 ⊆ wss 3129 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 |
This theorem is referenced by: ssun4 3301 elun2 3303 unv 3460 un00 3469 snsspr2 3741 snsstp3 3744 unexb 4442 rnexg 4892 brtpos0 6252 ac6sfi 6897 caserel 7085 pnfxr 8008 ltrelxr 8016 un0mulcl 9208 fsumsplit 11410 fprodsplitdc 11599 cnfldcj 13393 lgsdir2lem3 14362 bdunexb 14592 |
Copyright terms: Public domain | W3C validator |