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Mirrors > Home > ILE Home > Th. List > elind | Unicode version |
Description: Deduce membership in an intersection of two classes. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
elind.1 | |
elind.2 |
Ref | Expression |
---|---|
elind |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elind.1 | . 2 | |
2 | elind.2 | . 2 | |
3 | elin 3254 | . 2 | |
4 | 1, 2, 3 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1480 cin 3065 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-in 3072 |
This theorem is referenced by: elfir 6854 infpwfidom 7047 strslfv2d 11990 baspartn 12206 bastg 12219 isopn3 12283 restbasg 12326 lmss 12404 metrest 12664 tgioo 12704 dvmulxxbr 12824 pilem3 12853 |
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