Theorem 2i3 246

Description: Join both sides with Kalmbach implication.

Hypotheses

Ref	Expression
2i3.1	a = b
2i3.2	c = d

Assertion

Ref	Expression
2i3	(a ->3 c) = (b ->3 d)

Proof of Theorem 2i3

Step	Hyp	Ref	Expression
1		2i3.2	. . 3 c = d
2	1	li3 244	. 2 (a ->3 c) = (a ->3 d)
3		2i3.1	. . 3 a = b
4	3	ri3 245	. 2 (a ->3 d) = (b ->3 d)
5	2, 4	ax-r2 35	1 (a ->3 c) = (b ->3 d)

Syntax hints:   = wb 1   ->3 wi3 15

This theorem is referenced by:  i32i3 522  u3lemax4 778

This theorem was proved from axioms:  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-i3 45

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