Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > elrint | Unicode version |
Description: Membership in a restricted intersection. (Contributed by Stefan O'Rear, 3-Apr-2015.) |
Ref | Expression |
---|---|
elrint |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3155 | . 2 | |
2 | elintg 3644 | . . 3 | |
3 | 2 | pm5.32i 441 | . 2 |
4 | 1, 3 | bitri 182 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wcel 1433 wral 2348 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-ral 2353 df-v 2603 df-in 2979 df-int 3637 |
This theorem is referenced by: elrint2 3677 |
Copyright terms: Public domain | W3C validator |