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Mirrors > Home > ILE Home > Th. List > intssunim | Unicode version |
Description: The intersection of an inhabited set is a subclass of its union. (Contributed by NM, 29-Jul-2006.) |
Ref | Expression |
---|---|
intssunim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.2m 3449 | . . . 4 | |
2 | 1 | ex 114 | . . 3 |
3 | vex 2689 | . . . 4 | |
4 | 3 | elint2 3778 | . . 3 |
5 | eluni2 3740 | . . 3 | |
6 | 2, 4, 5 | 3imtr4g 204 | . 2 |
7 | 6 | ssrdv 3103 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wex 1468 wcel 1480 wral 2416 wrex 2417 wss 3071 cuni 3736 cint 3771 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 df-int 3772 |
This theorem is referenced by: intssuni2m 3795 |
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