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Theorem anandi 114
Description: Distribution of conjunction over conjunction.
Assertion
Ref Expression
anandi (a ^ (b ^ c)) = ((a ^ b) ^ (a ^ c))
Proof of Theorem anandi
StepHypRef Expression
1 anidm 111 . . . 4 (a ^ a) = a
21ax-r1 35 . . 3 a = (a ^ a)
32ran 78 . 2 (a ^ (b ^ c)) = ((a ^ a) ^ (b ^ c))
4 an4 86 . 2 ((a ^ a) ^ (b ^ c)) = ((a ^ b) ^ (a ^ c))
53, 4ax-r2 36 1 (a ^ (b ^ c)) = ((a ^ b) ^ (a ^ 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:  wwfh1  216  wdf-c2  384  wfh1  423  fh1  469  i3bi  496  u5lembi  725  u3lem13b  790  3vth9  812  mlaoml  833  comanblem1  870  oa3moa3  1029
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