Theorem unundir 2203

Description: Union distributes over itself.

Assertion

Ref	Expression
unundir	|- ((A u. B) u. C) = ((A u. C) u. (B u. C))

Proof of Theorem unundir

Step	Hyp	Ref	Expression
1		unidm 2186	. . 3 |- (C u. C) = C
2	1	uneq2i 2192	. 2 |- ((A u. B) u. (C u. C)) = ((A u. B) u. C)
3		un4 2201	. 2 |- ((A u. B) u. (C u. C)) = ((A u. C) u. (B u. C))
4	2, 3	eqtr3i 1504	1 |- ((A u. B) u. C) = ((A u. C) u. (B u. C))

Syntax hints:   = wceq 960   u. cun 2056

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 966  ax-gen 967  ax-8 968  ax-10 970  ax-12 972  ax-17 975  ax-4 977  ax-5o 979  ax-6o 982  ax-9o 1127  ax-10o 1144  ax-16 1214  ax-11o 1222  ax-ext 1464

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 985  df-sb 1176  df-clab 1470  df-cleq 1475  df-clel 1478  df-v 1819  df-un 2061

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