Theorem i3th4 528

Description: Theorem for Kalmbach implication.

Assertion

Ref	Expression
i3th4	(a ->3 (b ->3 b)) = 1

Proof of Theorem i3th4

Step	Hyp	Ref	Expression
1		i31 502	. 2 (a ->3 1) = 1
2		i3id 243	. . . . 5 (b ->3 b) = 1
3	2	ax-r1 34	. . . 4 1 = (b ->3 b)
4	3	li3 244	. . 3 (a ->3 1) = (a ->3 (b ->3 b))
5	4	rbi 90	. 2 ((a ->3 1) == 1) = ((a ->3 (b ->3 b)) == 1)
6	1, 5	wed 423	1 (a ->3 (b ->3 b)) = 1

Syntax hints:   = wb 1  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  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i3 45  df-le1 122  df-le2 123

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