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Theorem unidif0 4574
 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 4209 . . . 4
2 undif1 3833 . . . . . 6
3 uncom 3569 . . . . . 6
42, 3eqtr2i 2494 . . . . 5
54unieqi 4199 . . . 4
6 0ex 4528 . . . . . . 7
76unisn 4205 . . . . . 6
87uneq2i 3576 . . . . 5
9 un0 3762 . . . . 5
108, 9eqtr2i 2494 . . . 4
111, 5, 103eqtr4ri 2504 . . 3
12 uniun 4209 . . 3
137uneq1i 3575 . . 3
1411, 12, 133eqtri 2497 . 2
15 uncom 3569 . 2
16 un0 3762 . 2
1714, 15, 163eqtri 2497 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   cdif 3387   cun 3388  c0 3722  csn 3959  cuni 4190 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-nul 4527 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-sn 3960  df-pr 3962  df-uni 4191 This theorem is referenced by:  infeq5i  8159  zornn0g  8953  basdif0  20045  tgdif0  20085  omsmeas  29228  omsmeasOLD  29229  stoweidlem57  38030
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