Theorem 2i3 254

Description: Join both sides with Kalmbach implication. (Contributed by NM, 2-Nov-1997.)

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 252	. 2 (a →3 c) = (a →3 d)
3		2i3.1	. . 3 a = b
4	3	ri3 253	. 2 (a →3 d) = (b →3 d)
5	2, 4	ax-r2 36	1 (a →3 c) = (b →3 d)

Syntax hints:   = wb 1   →₃ wi3 14

This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-i3 46

This theorem is referenced by:  i32i3  540  u3lemax4  796