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Theorem wddi4 1108
Description: The weak distributive law in WDOL.
Assertion
Ref Expression
wddi4 (((a ^ b) v c) == ((a v c) ^ (b v c))) = 1
Proof of Theorem wddi4
StepHypRef Expression
1 wa2 192 . 2 (((a ^ b) v c) == (c v (a ^ b))) = 1
2 wddi3 1107 . . 3 ((c v (a ^ b)) == ((c v a) ^ (c v b))) = 1
3 wa2 192 . . . 4 ((c v a) == (a v c)) = 1
4 wa2 192 . . . 4 ((c v b) == (b v c)) = 1
53, 4w2an 373 . . 3 (((c v a) ^ (c v b)) == ((a v c) ^ (b v c))) = 1
62, 5wr2 371 . 2 ((c v (a ^ b)) == ((a v c) ^ (b v c))) = 1
71, 6wr2 371 1 (((a ^ b) v c) == ((a v c) ^ (b v c))) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5   v wo 6   ^ wa 7  1wt 8
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361  ax-wdol 1102
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131  df-cmtr 134
This theorem is referenced by:  wdid0id5  1109
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