Theorem anandir 115

Description: Distribution of conjunction over conjunction.

Assertion

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

Proof of Theorem anandir

Step	Hyp	Ref	Expression
1		anidm 111	. . . 4 (c ^ c) = c
2	1	ax-r1 35	. . 3 c = (c ^ c)
3	2	lan 77	. 2 ((a ^ b) ^ c) = ((a ^ b) ^ (c ^ c))
4		an4 86	. 2 ((a ^ b) ^ (c ^ c)) = ((a ^ c) ^ (b ^ c))
5	3, 4	ax-r2 36	1 ((a ^ b) ^ c) = ((a ^ c) ^ (b ^ c))

Syntax hints:   = wb 1   ^ wa 7

This theorem is referenced by:  leran 153  ka4lemo 228  wr5-2v 366  wleran 394  ska4 433  i3orlem5 556  ud2lem1 563  mlaoml 833  comanblem2 871  e2astlem1 895  oath1 1004  4oath1 1040  lem3.3.6 1055

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

Copyright terms: Public domain