Theorem i3i0 513

Description: Translation from Kalmbach implication. (Contributed by NM, 9-Nov-1997.)

Hypothesis

Ref	Expression
i3i0.1	(a →3 (a →3 b)) = 1

Assertion

Ref	Expression
i3i0	(a⊥ ∪ b) = 1

Proof of Theorem i3i0

Step	Hyp	Ref	Expression
1		lem4 511	. . 3 (a →3 (a →3 b)) = (a⊥ ∪ b)
2	1	ax-r1 35	. 2 (a⊥ ∪ b) = (a →3 (a →3 b))
3		i3i0.1	. 2 (a →3 (a →3 b)) = 1
4	2, 3	ax-r2 36	1 (a⊥ ∪ b) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6  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  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  i0i3tr  541  i3i0tr  542