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Theorem ledir 175
Description: Half of distributive law.
Assertion
Ref Expression
ledir ((b ^ a) v (c ^ a)) =< ((b v c) ^ a)
Proof of Theorem ledir
StepHypRef Expression
1 ledi 174 . 2 ((a ^ b) v (a ^ c)) =< (a ^ (b v c))
2 ancom 74 . . 3 (b ^ a) = (a ^ b)
3 ancom 74 . . 3 (c ^ a) = (a ^ c)
42, 32or 72 . 2 ((b ^ a) v (c ^ a)) = ((a ^ b) v (a ^ c))
5 ancom 74 . 2 ((b v c) ^ a) = (a ^ (b v c))
61, 4, 5le3tr1 140 1 ((b ^ a) v (c ^ a)) =< ((b v c) ^ a)
Colors of variables: term
Syntax hints:   =< wle 2   v wo 6   ^ 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  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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