![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > elun2 | GIF version |
Description: Membership law for union of classes. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
elun2 | ⊢ (𝐴 ∈ 𝐵 → 𝐴 ∈ (𝐶 ∪ 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun2 3167 | . 2 ⊢ 𝐵 ⊆ (𝐶 ∪ 𝐵) | |
2 | 1 | sseli 3024 | 1 ⊢ (𝐴 ∈ 𝐵 → 𝐴 ∈ (𝐶 ∪ 𝐵)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1439 ∪ cun 3000 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2624 df-un 3006 df-in 3008 df-ss 3015 |
This theorem is referenced by: dcun 3398 exmidundif 4045 exmidundifim 4046 dftpos4 6044 tfrlemibxssdm 6108 tfrlemi14d 6114 tfr1onlembxssdm 6124 tfr1onlemres 6130 tfrcllembxssdm 6137 tfrcllemres 6143 dcdifsnid 6279 findcard2d 6663 findcard2sd 6664 onunsnss 6683 undifdcss 6689 fisseneq 6698 fidcenumlemrks 6718 djurclr 6798 djurcl 6800 djuss 6817 finomni 6859 mnfxr 7607 hashinfuni 10248 fsumsplitsnun 10876 sumsplitdc 10889 modfsummodlem1 10913 srnginvld 11683 lmodvscad 11694 ipsscad 11702 ipsvscad 11703 ipsipd 11704 |
Copyright terms: Public domain | W3C validator |