Theorem i3abs2 523

Description: Antecedent absorption. (Contributed by NM, 9-Nov-1997.)

Hypothesis

Ref	Expression
i3abs2.1	(a →3 (a →3 (a →3 b))) = 1

Assertion

Ref	Expression
i3abs2	(a →3 (a →3 b)) = 1

Proof of Theorem i3abs2

Step	Hyp	Ref	Expression
1		i3abs2.1	. 2 (a →3 (a →3 (a →3 b))) = 1
2		i3abs1 522	. . 3 (a →3 (a →3 (a →3 b))) = (a →3 (a →3 b))
3	2	bi1 118	. 2 ((a →3 (a →3 (a →3 b))) ≡ (a →3 (a →3 b))) = 1
4	1, 3	wwbmp 205	1 (a →3 (a →3 b)) = 1

Syntax hints:   = wb 1  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)