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Theorem uni0 3598
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  U. (/)  (/)

Proof of Theorem uni0
StepHypRef Expression
1 0ss 3249 . 2  (/)  C_  { (/) }
2 uni0b 3596 . 2  U. (/)  (/)  (/)  C_  { (/) }
31, 2mpbir 134 1  U. (/)  (/)
Colors of variables: wff set class
Syntax hints:   wceq 1242    C_ wss 2911   (/)c0 3218   {csn 3367   U.cuni 3571
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-dif 2914  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-uni 3572
This theorem is referenced by:  iununir  3729  unixp0im  4797  iotanul  4825  1st0  5713  2nd0  5714  brtpos0  5808  tpostpos  5820
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