Theorem unidm 3324

Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem unidm

Dummy variable x is distinct from all other variables.

Step	Hyp	Ref	Expression
1		oridm 759	. 2 |- ( ( x e. A \/ x e. A ) <-> x e. A )
2	1	uneqri 3323	1 |- ( A u. A ) = A

Syntax hints:   = wceq 1373   e. wcel 2178   u. cun 3172

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178

This theorem is referenced by:  unundi  3342  unundir  3343  uneqin  3432  difabs  3445  ifidss  3595  dfsn2  3657  diftpsn3  3785  unisn  3880  dfdm2  5236  fun2  5470  resasplitss  5477  xpider  6716  pm54.43  7324  plyun0  15323