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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 3229 | . 2 | |
4 | 1, 2, 3 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 cin 3040 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 |
This theorem is referenced by: elfir 6829 infpwfidom 7022 strslfv2d 11912 baspartn 12128 bastg 12141 isopn3 12205 restbasg 12248 lmss 12326 metrest 12586 tgioo 12626 dvmulxxbr 12746 pilem3 12775 |
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