Theorem u2lemc5 697

Description: Commutation theorem for Dishkant implication. (Contributed by NM, 11-Jan-1998.)

Hypothesis

Ref	Expression
ulemc3.1	a C b

Assertion

Ref	Expression
u2lemc5	a C (a →2 b)

Proof of Theorem u2lemc5

Step	Hyp	Ref	Expression
1		comid 187	. 2 a C a
2		ulemc3.1	. 2 a C b
3	1, 2	u2lemc2 687	1 a C (a →2 b)

Syntax hints:   C wc 3   →₂ wi2 13

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-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by: (None)