Theorem oa4cl 1007

Description: 4-variable OA closed equational form)

Assertion

Ref	Expression
oa4cl	((a v (b ^ a_|_)) ^ (c v (d ^ c_|_))) =< ((b ^ a_|_) v (a ^ (c v ((a v c) ^ ((b ^ a_|_) v (d ^ c_|_))))))

Proof of Theorem oa4cl

Step	Hyp	Ref	Expression
1		leor 151	. . 3 a =< (b_|_ v a)
2		oran2 84	. . 3 (b_|_ v a) = (b ^ a_|_)_|_
3	1, 2	lbtr 131	. 2 a =< (b ^ a_|_)_|_
4		leor 151	. . 3 c =< (d_|_ v c)
5		oran2 84	. . 3 (d_|_ v c) = (d ^ c_|_)_|_
6	4, 5	lbtr 131	. 2 c =< (d ^ c_|_)_|_
7	3, 6	ax-oal4 1006	1 ((a v (b ^ a_|_)) ^ (c v (d ^ c_|_))) =< ((b ^ a_|_) v (a ^ (c v ((a v c) ^ ((b ^ a_|_) v (d ^ c_|_))))))

Syntax hints:   =< wle 2  _|_wn 4   v wo 6   ^ wa 7

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  ax-oal4 1006

This theorem depends on definitions:  df-a 39  df-le1 122  df-le2 123

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