Theorem distoah1 940

Description: Satisfaction of distributive law hypothesis. (Contributed by NM, 29-Nov-1998.)

Hypotheses

Ref	Expression
distoa.1	d = (a →2 b)
distoa.2	e = ((b ∪ c) →1 ((a →2 b) ∩ (a →2 c)))
distoa.3	f = ((b ∪ c) →2 ((a →2 b) ∩ (a →2 c)))

Assertion

Ref	Expression
distoah1	d ≤ (a →2 b)

Proof of Theorem distoah1

Step	Hyp	Ref	Expression
1		distoa.1	. 2 d = (a →2 b)
2	1	bile 142	1 d ≤ (a →2 b)

Syntax hints:   = wb 1   ≤ wle 2   ∪ wo 6   ∩ wa 7   →₁ wi1 12   →₂ wi2 13

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-t 41  df-f 42  df-le1 130

This theorem is referenced by: (None)