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Mirrors > Home > ILE Home > Th. List > elinel1 | Unicode version |
Description: Membership in an intersection implies membership in the first set. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
elinel1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3304 | . 2 | |
2 | 1 | simplbi 272 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2136 cin 3114 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2296 df-v 2727 df-in 3121 |
This theorem is referenced by: elin1d 3310 fival 6931 fi0 6936 blbas 13033 blres 13034 pilem3 13304 taupi 13896 |
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