Theorem unundi 2191

Description: Union distributes over itself.

Assertion

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

Proof of Theorem unundi

Step	Hyp	Ref	Expression
1		unidm 2175	. . 3 |- (A u. A) = A
2	1	uneq1i 2180	. 2 |- ((A u. A) u. (B u. C)) = (A u. (B u. C))
3		un4 2190	. 2 |- ((A u. A) u. (B u. C)) = ((A u. B) u. (A u. C))
4	2, 3	eqtr3 1497	1 |- (A u. (B u. C)) = ((A u. B) u. (A u. C))

Syntax hints:   = wceq 956   u. cun 2045

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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