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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 3821 | . 2 | |
2 | dfss3 3137 | . 2 | |
3 | velsn 3600 | . . 3 | |
4 | 3 | ralbii 2476 | . 2 |
5 | 1, 2, 4 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1348 wcel 2141 wral 2448 wss 3121 c0 3414 csn 3583 cuni 3796 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-dif 3123 df-in 3127 df-ss 3134 df-nul 3415 df-sn 3589 df-uni 3797 |
This theorem is referenced by: (None) |
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