Theorem unidm 2175

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 243	. 2 |- ((x e. A \/ x e. A) <-> x e. A)
2	1	uneqri 2174	1 |- (A u. A) = A

Syntax hints:   = wceq 956   e. wcel 958   u. cun 2045

This theorem is referenced by:  unundi 2191  unundir 2192  uneqin 2256  dfsn2 2420  unisn 2517  mapunen 4502  pm54.43 4572

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050

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