Theorem i3th6 548

Description: Theorem for Kalmbach implication. (Contributed by NM, 16-Nov-1997.)

Assertion

Ref	Expression
i3th6	((a →3 (a →3 (a →3 b))) →3 (a →3 (a →3 b))) = 1

Proof of Theorem i3th6

Step	Hyp	Ref	Expression
1		i3abs1 522	. . 3 (a →3 (a →3 (a →3 b))) = (a →3 (a →3 b))
2	1	bi1 118	. 2 ((a →3 (a →3 (a →3 b))) ≡ (a →3 (a →3 b))) = 1
3		bii3 516	. 2 (((a →3 (a →3 (a →3 b))) ≡ (a →3 (a →3 b))) →3 ((a →3 (a →3 (a →3 b))) →3 (a →3 (a →3 b)))) = 1
4	2, 3	skmp3 245	1 ((a →3 (a →3 (a →3 b))) →3 (a →3 (a →3 b))) = 1

Syntax hints:   = wb 1   ≡ tb 5  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: (None)