Theorem u2lemc5 679

Description: Commutation theorem for Dishkant implication.

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 179	. 2 a C a
2		ulemc3.1	. 2 a C b
3	1, 2	u2lemc2 669	1 a C (a ->2 b)

Syntax hints:   C wc 3   ->2 wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i2 44  df-le1 122  df-le2 123  df-c1 124  df-c2 125

metamath.org