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Theorem uneq2 3085
Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
uneq2  C  u.  C  u.

Proof of Theorem uneq2
StepHypRef Expression
1 uneq1 3084 . 2  u.  C  u.  C
2 uncom 3081 . 2  C  u.  u.  C
3 uncom 3081 . 2  C  u.  u.  C
41, 2, 33eqtr4g 2094 1  C  u.  C  u.
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242    u. cun 2909
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-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-bndl 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-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916
This theorem is referenced by:  uneq12  3086  uneq2i  3088  uneq2d  3091  uneqin  3182  disjssun  3279  uniprg  3586  sucprc  4115  unexb  4143  bdunexb  9375  bj-unexg  9376
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