Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > intun | Unicode version |
Description: The class intersection of the union of two classes. Theorem 78 of [Suppes] p. 42. (Contributed by NM, 22-Sep-2002.) |
Ref | Expression |
---|---|
intun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1410 | . . . 4 | |
2 | elun 3113 | . . . . . . 7 | |
3 | 2 | imbi1i 236 | . . . . . 6 |
4 | jaob 663 | . . . . . 6 | |
5 | 3, 4 | bitri 182 | . . . . 5 |
6 | 5 | albii 1399 | . . . 4 |
7 | vex 2604 | . . . . . 6 | |
8 | 7 | elint 3642 | . . . . 5 |
9 | 7 | elint 3642 | . . . . 5 |
10 | 8, 9 | anbi12i 447 | . . . 4 |
11 | 1, 6, 10 | 3bitr4i 210 | . . 3 |
12 | 7 | elint 3642 | . . 3 |
13 | elin 3155 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 210 | . 2 |
15 | 14 | eqriv 2078 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wo 661 wal 1282 wceq 1284 wcel 1433 cun 2971 cin 2972 cint 3636 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-un 2977 df-in 2979 df-int 3637 |
This theorem is referenced by: intunsn 3674 riinint 4611 |
Copyright terms: Public domain | W3C validator |