Theorem wddi3 1109

Description: The weak distributive law in WDOL. (Contributed by NM, 5-Mar-2006.)

Assertion

Ref	Expression
wddi3	((a ∪ (b ∩ c)) ≡ ((a ∪ b) ∩ (a ∪ c))) = 1

Proof of Theorem wddi3

Step	Hyp	Ref	Expression
1		wdcom 1105	. 2 C (a, b) = 1
2		wdcom 1105	. 2 C (a, c) = 1
3	1, 2	wfh3 425	1 ((a ∪ (b ∩ c)) ≡ ((a ∪ b) ∩ (a ∪ c))) = 1

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 1104

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:  wddi4  1110  wdid0id5  1111  wdid0id1  1112  wdid0id2  1113  wdid0id3  1114  wdid0id4  1115