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Theorem wddi2 1106
 Description: The weak distributive law in WDOL.
Assertion
Ref Expression
wddi2 (((ab) ∩ c) ≡ ((ac) ∪ (bc))) = 1

Proof of Theorem wddi2
StepHypRef Expression
1 wancom 203 . 2 (((ab) ∩ c) ≡ (c ∩ (ab))) = 1
2 wddi1 1105 . . 3 ((c ∩ (ab)) ≡ ((ca) ∪ (cb))) = 1
3 wancom 203 . . . 4 ((ca) ≡ (ac)) = 1
4 wancom 203 . . . 4 ((cb) ≡ (bc)) = 1
53, 4w2or 372 . . 3 (((ca) ∪ (cb)) ≡ ((ac) ∪ (bc))) = 1
62, 5wr2 371 . 2 ((c ∩ (ab)) ≡ ((ac) ∪ (bc))) = 1
71, 6wr2 371 1 (((ab) ∩ c) ≡ ((ac) ∪ (bc))) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≡ tb 5   ∪ 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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