Theorem unidm 1603

Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27.

Assertion

Ref	Expression
unidm	|- (A u. A) = A

Proof of Theorem unidm

Step	Hyp	Ref	Expression
1		oridm 208	. 2 |- ((x e. A \/ x e. A) <-> x e. A)
2	1	uneqri 1602	1 |- (A u. A) = A

Syntax hints:   = wceq 1091   e. wcel 1092   u. cun 1485

This theorem is referenced by:  unundi 1619  unundir 1620  dfsn2 1819  unisn 1932  mapunen 3397

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490

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