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Theorem unidif0 4374
 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 4036 . . . 4
2 undif1 3705 . . . . . 6
3 uncom 3493 . . . . . 6
42, 3eqtr2i 2459 . . . . 5
54unieqi 4027 . . . 4
6 0ex 4341 . . . . . . 7
76unisn 4033 . . . . . 6
87uneq2i 3500 . . . . 5
9 un0 3654 . . . . 5
108, 9eqtr2i 2459 . . . 4
111, 5, 103eqtr4ri 2469 . . 3
12 uniun 4036 . . 3
137uneq1i 3499 . . 3
1411, 12, 133eqtri 2462 . 2
15 uncom 3493 . 2
16 un0 3654 . 2
1714, 15, 163eqtri 2462 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   cdif 3319   cun 3320  c0 3630  csn 3816  cuni 4017 This theorem is referenced by:  infeq5i  7593  zornn0g  8387  basdif0  17020  tgdif0  17059  stoweidlem57  27784 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-nul 4340 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-sn 3822  df-pr 3823  df-uni 4018
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