Theorem oa4ctob 947

Description: Derivation of 4-OA law variant.

Hypothesis

Ref	Expression
oa4ctob.1	(a_|_ ^ (a v (c ^ (((a ^ c) v ((a ->1 g) ^ (c ->1 g))) v (((a ^ e) v ((a ->1 g) ^ (e ->1 g))) ^ ((c ^ e) v ((c ->1 g) ^ (e ->1 g)))))))) =< g

Assertion

Ref	Expression
oa4ctob	((a ->1 g) ^ (a v (c ^ (((a ^ c) v ((a ->1 g) ^ (c ->1 g))) v (((a ^ e) v ((a ->1 g) ^ (e ->1 g))) ^ ((c ^ e) v ((c ->1 g) ^ (e ->1 g)))))))) =< g

Proof of Theorem oa4ctob

Step	Hyp	Ref	Expression
1		oa4ctob.1	. 2 (a_|_ ^ (a v (c ^ (((a ^ c) v ((a ->1 g) ^ (c ->1 g))) v (((a ^ e) v ((a ->1 g) ^ (e ->1 g))) ^ ((c ^ e) v ((c ->1 g) ^ (e ->1 g)))))))) =< g
2	1	oas 905	1 ((a ->1 g) ^ (a v (c ^ (((a ^ c) v ((a ->1 g) ^ (c ->1 g))) v (((a ^ e) v ((a ->1 g) ^ (e ->1 g))) ^ ((c ^ e) v ((c ->1 g) ^ (e ->1 g)))))))) =< g

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

This theorem is referenced by:  axoa4b 1014

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-le1 122  df-le2 123  df-c1 124  df-c2 125

metamath.org