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Theorem unidif0 4625
 Description: The removal of the empty set from a class does not affect its union. (Contributed by NM, 22-Mar-2004.)
Assertion
Ref Expression
unidif0

Proof of Theorem unidif0
StepHypRef Expression
1 uniun 4268 . . . 4
2 undif1 3903 . . . . . 6
3 uncom 3647 . . . . . 6
42, 3eqtr2i 2487 . . . . 5
54unieqi 4258 . . . 4
6 0ex 4582 . . . . . . 7
76unisn 4264 . . . . . 6
87uneq2i 3654 . . . . 5
9 un0 3810 . . . . 5
108, 9eqtr2i 2487 . . . 4
111, 5, 103eqtr4ri 2497 . . 3
12 uniun 4268 . . 3
137uneq1i 3653 . . 3
1411, 12, 133eqtri 2490 . 2
15 uncom 3647 . 2
16 un0 3810 . 2
1714, 15, 163eqtri 2490 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  \cdif 3472  u.cun 3473   c0 3784  {csn 4029  U.cuni 4249 This theorem is referenced by:  infeq5i  8074  zornn0g  8906  basdif0  19454  tgdif0  19494  stoweidlem57  31839 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032  df-uni 4250
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