Theorem u3lemc2 688

Description: Commutation theorem for Kalmbach implication. (Contributed by NM, 14-Dec-1997.)

Hypotheses

Ref	Expression
ulemc2.1	a C b
ulemc2.2	a C c

Assertion

Ref	Expression
u3lemc2	a C (b →3 c)

Proof of Theorem u3lemc2

Step	Hyp	Ref	Expression
1		ulemc2.1	. 2 a C b
2		ulemc2.2	. 2 a C c
3	1, 2	com2i3 509	1 a C (b →3 c)

Syntax hints:   C wc 3   →₃ wi3 14

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by:  u3lem2  746