Theorem i3th4 546

Description: Theorem for Kalmbach implication. (Contributed by NM, 7-Nov-1997.)

Assertion

Ref	Expression
i3th4	(a →3 (b →3 b)) = 1

Proof of Theorem i3th4

Step	Hyp	Ref	Expression
1		i31 520	. 2 (a →3 1) = 1
2		i3id 251	. . . . 5 (b →3 b) = 1
3	2	ax-r1 35	. . . 4 1 = (b →3 b)
4	3	li3 252	. . 3 (a →3 1) = (a →3 (b →3 b))
5	4	rbi 98	. 2 ((a →3 1) ≡ 1) = ((a →3 (b →3 b)) ≡ 1)
6	1, 5	wed 441	1 (a →3 (b →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

This theorem is referenced by: (None)