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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 3254 | . 2 | |
2 | 1 | simplbi 272 | 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: elin1d 3260 fival 6851 fi0 6856 blbas 12591 blres 12592 pilem3 12853 taupi 13228 |
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