Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > undifss | Unicode version |
Description: Union of complementary parts into whole. (Contributed by Jim Kingdon, 4-Aug-2018.) |
Ref | Expression |
---|---|
undifss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difss 3070 | . . . 4 | |
2 | 1 | jctr 298 | . . 3 |
3 | unss 3117 | . . 3 | |
4 | 2, 3 | sylib 127 | . 2 |
5 | ssun1 3106 | . . 3 | |
6 | sstr 2953 | . . 3 | |
7 | 5, 6 | mpan 400 | . 2 |
8 | 4, 7 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 cdif 2914 cun 2915 wss 2917 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 |
This theorem is referenced by: difsnss 3510 |
Copyright terms: Public domain | W3C validator |