Theorem anandi 114

Description: Distribution of conjunction over conjunction.

Assertion

Ref	Expression
anandi	(a ^ (b ^ c)) = ((a ^ b) ^ (a ^ c))

Proof of Theorem anandi

Step	Hyp	Ref	Expression
1		anidm 111	. . . 4 (a ^ a) = a
2	1	ax-r1 35	. . 3 a = (a ^ a)
3	2	ran 78	. 2 (a ^ (b ^ c)) = ((a ^ a) ^ (b ^ c))
4		an4 86	. 2 ((a ^ a) ^ (b ^ c)) = ((a ^ b) ^ (a ^ c))
5	3, 4	ax-r2 36	1 (a ^ (b ^ c)) = ((a ^ b) ^ (a ^ c))

Syntax hints:   = wb 1   ^ wa 7

This theorem is referenced by:  wwfh1 216  wdf-c2 384  wfh1 423  fh1 469  i3bi 496  u5lembi 725  u3lem13b 790  3vth9 812  mlaoml 833  comanblem1 870

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42

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