Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ineqri | Unicode version |
Description: Inference from membership to intersection. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
ineqri.1 |
Ref | Expression |
---|---|
ineqri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3291 | . . 3 | |
2 | ineqri.1 | . . 3 | |
3 | 1, 2 | bitri 183 | . 2 |
4 | 3 | eqriv 2154 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 wcel 2128 cin 3101 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-in 3108 |
This theorem is referenced by: inidm 3317 inass 3318 indi 3355 inab 3376 in0 3429 pwin 4245 dmres 4890 |
Copyright terms: Public domain | W3C validator |