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Mirrors > Home > ILE Home > Th. List > uni0c | Unicode version |
Description: The union of a set is empty iff all of its members are empty. (Contributed by NM, 16-Aug-2006.) |
Ref | Expression |
---|---|
uni0c |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uni0b 3797 | . 2 | |
2 | dfss3 3118 | . 2 | |
3 | velsn 3577 | . . 3 | |
4 | 3 | ralbii 2463 | . 2 |
5 | 1, 2, 4 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1335 wcel 2128 wral 2435 wss 3102 c0 3394 csn 3560 cuni 3772 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-in 3108 df-ss 3115 df-nul 3395 df-sn 3566 df-uni 3773 |
This theorem is referenced by: (None) |
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