Theorem distoah1 920

Description: Satisfaction of distributive law hypothesis.

Hypotheses

Ref	Expression
distoa.1	d = (a ->2 b)
distoa.2	e = ((b v c) ->1 ((a ->2 b) ^ (a ->2 c)))
distoa.3	f = ((b v 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 134	1 d =< (a ->2 b)

Syntax hints:   = wb 1   =< wle 2   v wo 6   ^ wa 7   ->1 wi1 13   ->2 wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-t 40  df-f 41  df-le1 122

metamath.org