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Theorem wddi2 1106
Description: The weak distributive law in WDOL.
Assertion
Ref Expression
wddi2 (((a v b) ^ c) == ((a ^ c) v (b ^ c))) = 1
Proof of Theorem wddi2
StepHypRef Expression
1 wancom 203 . 2 (((a v b) ^ c) == (c ^ (a v b))) = 1
2 wddi1 1105 . . 3 ((c ^ (a v b)) == ((c ^ a) v (c ^ b))) = 1
3 wancom 203 . . . 4 ((c ^ a) == (a ^ c)) = 1
4 wancom 203 . . . 4 ((c ^ b) == (b ^ c)) = 1
53, 4w2or 372 . . 3 (((c ^ a) v (c ^ b)) == ((a ^ c) v (b ^ c))) = 1
62, 5wr2 371 . 2 ((c ^ (a v b)) == ((a ^ c) v (b ^ c))) = 1
71, 6wr2 371 1 (((a v b) ^ c) == ((a ^ c) v (b ^ 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: (None)
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