Theorem i3btr 528

Description: Transitive inference. (Contributed by NM, 7-Nov-1997.)

Hypotheses

Ref	Expression
i3btr.1	(a →3 b) = 1
i3btr.2	b = c

Assertion

Ref	Expression
i3btr	(a →3 c) = 1

Proof of Theorem i3btr

Step	Hyp	Ref	Expression
1		i3btr.1	. 2 (a →3 b) = 1
2		i3btr.2	. . . 4 b = c
3	2	li3 252	. . 3 (a →3 b) = (a →3 c)
4	3	bi1 118	. 2 ((a →3 b) ≡ (a →3 c)) = 1
5	1, 4	wwbmp 205	1 (a →3 c) = 1

Syntax hints:   = wb 1  1wt 8   →₃ wi3 14

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46

This theorem is referenced by:  i33tr1  529