Theorem mccune3 240

Description: E3 - OL theorem proved by EQP

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 45	. . . . 5 (a →3 b) = (((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))
2	1	ax-r1 34	. . . 4 (((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b))) = (a →3 b)
3	2	ax-r4 36	. . 3 (((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ = (a →3 b)⊥
4	3	ax-r5 37	. 2 ((((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ ∪ (a⊥ ∪ b)) = ((a →3 b)⊥ ∪ (a⊥ ∪ b))
5		ska15 236	. 2 ((a →3 b)⊥ ∪ (a⊥ ∪ b)) = 1
6	4, 5	ax-r2 35	1 ((((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) ∪ (a ∩ (a⊥ ∪ b)))⊥ ∪ (a⊥ ∪ b)) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 9   →₃ wi3 15

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

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-i3 45  df-le1 122  df-le2 123

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