Theorem wddi-0 1117

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

Assertion

Ref	Expression
wddi-0	((a ∩ (b ∪ c)) ≡0 ((a ∩ b) ∪ (a ∩ c))) = 1

Proof of Theorem wddi-0

Step	Hyp	Ref	Expression
1		wddi1 1107	. 2 ((a ∩ (b ∪ c)) ≡ ((a ∩ b) ∪ (a ∩ c))) = 1
2	1	id5id0 352	1 ((a ∩ (b ∪ c)) ≡0 ((a ∩ b) ∪ (a ∩ c))) = 1

Syntax hints:   = wb 1   ∪ wo 6   ∩ wa 7  1wt 8   ≡₀ wid0 17

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-id0 49  df-le 129  df-le1 130  df-le2 131  df-cmtr 134

This theorem is referenced by:  wddi-1  1118  wddi-2  1119  wddi-3  1120  wddi-4  1121