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Theorem uni0c 3762
 Description: The union of a set is empty iff all of its members are empty. (Contributed by NM, 16-Aug-2006.)
Assertion
Ref Expression
uni0c
Distinct variable group:   ,

Proof of Theorem uni0c
StepHypRef Expression
1 uni0b 3761 . 2
2 dfss3 3087 . 2
3 velsn 3544 . . 3
43ralbii 2441 . 2
51, 2, 43bitri 205 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1331   wcel 1480  wral 2416   wss 3071  c0 3363  csn 3527  cuni 3736 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 603  ax-in2 604  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-fal 1337  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-dif 3073  df-in 3077  df-ss 3084  df-nul 3364  df-sn 3533  df-uni 3737 This theorem is referenced by: (None)
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