Theorem unidm 3646

Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27. (Contributed by NM, 21-Jun-1993.)

Assertion

Ref	Expression
unidm

Proof of Theorem unidm

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		oridm 514	. 2
2	1	uneqri 3645	1

Syntax hints:  =wceq 1395  e.wcel 1818  u.cun 3473

This theorem is referenced by:  unundi  3664  unundir  3665  uneqin  3748  difabs  3761  undifabs  3905  dfif5  3957  dfsn2  4042  diftpsn3  4168  unisn  4264  dfdm2  5544  unixpid  5547  fun2  5754  resasplit  5760  xpider  7401  pm54.43  8402  lefld  15856  symg2bas  16423  gsumzaddlem  16934  pwssplit1  17705  plyun0  22594  constr3trllem3  24652  sseqf  28331  probun  28358  filnetlem3  30198  mapfzcons  30648  diophin  30706  pwssplit4  31035  fiuneneq  31154  compne  31349

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

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-v 3111  df-un 3480