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Theorem anandir 115
Description: Distribution of conjunction over conjunction.
Assertion
Ref Expression
anandir ((a ^ b) ^ c) = ((a ^ c) ^ (b ^ c))
Proof of Theorem anandir
StepHypRef Expression
1 anidm 111 . . . 4 (c ^ c) = c
21ax-r1 35 . . 3 c = (c ^ c)
32lan 77 . 2 ((a ^ b) ^ c) = ((a ^ b) ^ (c ^ c))
4 an4 86 . 2 ((a ^ b) ^ (c ^ c)) = ((a ^ c) ^ (b ^ c))
53, 4ax-r2 36 1 ((a ^ b) ^ c) = ((a ^ c) ^ (b ^ c))
Colors of variables: term
Syntax hints:   = wb 1   ^ wa 7
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
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  1041  lem3.3.6  1056
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