Theorem wddi1 1107

Description: Prove the weak distributive law in WDOL. This is our first WDOL theorem making use of ax-wom 361, which is justified by wdwom 1106. (Contributed by NM, 4-Mar-2006.)

Assertion

Ref	Expression
wddi1	((a ∩ (b ∪ c)) ≡ ((a ∩ b) ∪ (a ∩ c))) = 1

Proof of Theorem wddi1

Step	Hyp	Ref	Expression
1		wdcom 1105	. 2 C (a, b) = 1
2		wdcom 1105	. 2 C (a, c) = 1
3	1, 2	wfh1 423	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:  wddi2  1108  wddi-0  1117