Theorem mccune3 248

Description: E3 - OL theorem proved by EQP. (Contributed by NM, 14-Nov-1998.)

Assertion

Ref	Expression
mccune3	((((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ ∪ (a⊥ ∪ b)) = 1

Proof of Theorem mccune3

Step	Hyp	Ref	Expression
1		df-i3 46	. . . . 5 (a →3 b) = (((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))
2	1	ax-r1 35	. . . 4 (((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b))) = (a →3 b)
3	2	ax-r4 37	. . 3 (((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ = (a →3 b)⊥
4	3	ax-r5 38	. 2 ((((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ ∪ (a⊥ ∪ b)) = ((a →3 b)⊥ ∪ (a⊥ ∪ b))
5		ska15 244	. 2 ((a →3 b)⊥ ∪ (a⊥ ∪ b)) = 1
6	4, 5	ax-r2 36	1 ((((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ ∪ (a⊥ ∪ b)) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →₃ wi3 14

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131

This theorem is referenced by: (None)