Theorem i33tr2 512

Description: Transitive inference useful for eliminating definitions.

Hypotheses

Ref	Expression
i33tr2.1	(a ->3 b) = 1
i33tr2.2	a = c
i33tr2.3	b = d

Assertion

Ref	Expression
i33tr2	(c ->3 d) = 1

Proof of Theorem i33tr2

Step	Hyp	Ref	Expression
1		i33tr2.1	. 2 (a ->3 b) = 1
2		i33tr2.2	. . 3 a = c
3	2	ax-r1 34	. 2 c = a
4		i33tr2.3	. . 3 b = d
5	4	ax-r1 34	. 2 d = b
6	1, 3, 5	i33tr1 511	1 (c ->3 d) = 1

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

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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