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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 3490 | . . . 4 | |
2 | 1 | ex 114 | . . 3 |
3 | vex 2724 | . . . 4 | |
4 | 3 | elint2 3825 | . . 3 |
5 | eluni2 3787 | . . 3 | |
6 | 2, 4, 5 | 3imtr4g 204 | . 2 |
7 | 6 | ssrdv 3143 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wex 1479 wcel 2135 wral 2442 wrex 2443 wss 3111 cuni 3783 cint 3818 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-in 3117 df-ss 3124 df-uni 3784 df-int 3819 |
This theorem is referenced by: intssuni2m 3842 |
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