Theorem bi3tr 509

Description: Transitive inference.

Hypotheses

Ref	Expression
bi3tr.1	a = b
bi3tr.2	(b ->3 c) = 1

Assertion

Ref	Expression
bi3tr	(a ->3 c) = 1

Proof of Theorem bi3tr

Step	Hyp	Ref	Expression
1		bi3tr.2	. 2 (b ->3 c) = 1
2		bi3tr.1	. . . 4 a = b
3	2	ri3 245	. . 3 (a ->3 c) = (b ->3 c)
4	3	bi1 110	. 2 ((a ->3 c) == (b ->3 c)) = 1
5	1, 4	wwbmpr 198	1 (a ->3 c) = 1

Syntax hints:   = wb 1  1wt 9   ->3 wi3 15

This theorem is referenced by:  i33tr1 511

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

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

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