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Theorem uni0 3758
 Description: The union of the empty set is the empty set. Theorem 8.7 of [Quine] p. 54. (Reproved without relying on ax-nul by Eric Schmidt.) (Contributed by NM, 16-Sep-1993.) (Revised by Eric Schmidt, 4-Apr-2007.)
Assertion
Ref Expression
uni0

Proof of Theorem uni0
StepHypRef Expression
1 0ss 3396 . 2
2 uni0b 3756 . 2
31, 2mpbir 145 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   wss 3066  c0 3358  csn 3522  cuni 3731 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 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420  df-v 2683  df-dif 3068  df-in 3072  df-ss 3079  df-nul 3359  df-sn 3528  df-uni 3732 This theorem is referenced by:  iununir  3891  nnpredcl  4531  unixp0im  5070  iotanul  5098  1st0  6035  2nd0  6036  brtpos0  6142  tpostpos  6154  nnsucuniel  6384  sup00  6883  0opn  12162
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