Theorem oa6to4h2 936

Description: Satisfaction of 6-variable OA law hypothesis.

Hypotheses

Ref	Expression
oa6to4.1	b_|_ = (a ->1 g)_|_
oa6to4.2	d_|_ = (c ->1 g)_|_
oa6to4.3	f_|_ = (e ->1 g)_|_

Assertion

Ref	Expression
oa6to4h2	c_|_ =< d_|__|_

Proof of Theorem oa6to4h2

Step	Hyp	Ref	Expression
1		leo 150	. 2 c_|_ =< (c_|_ v (c ^ g))
2		oa6to4.2	. . . . 5 d_|_ = (c ->1 g)_|_
3		df-i1 43	. . . . . 6 (c ->1 g) = (c_|_ v (c ^ g))
4	3	ax-r4 36	. . . . 5 (c ->1 g)_|_ = (c_|_ v (c ^ g))_|_
5	2, 4	ax-r2 35	. . . 4 d_|_ = (c_|_ v (c ^ g))_|_
6	5	ax-r1 34	. . 3 (c_|_ v (c ^ g))_|_ = d_|_
7	6	con3 65	. 2 (c_|_ v (c ^ g)) = d_|__|_
8	1, 7	lbtr 131	1 c_|_ =< d_|__|_

Syntax hints:   = wb 1   =< wle 2  _|_wn 4   v wo 6   ^ wa 7   ->1 wi1 13

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-a 39  df-i1 43  df-le1 122  df-le2 123

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