Theorem wcomcom 414

Description: Commutation is symmetric. Kalmbach 83 p. 22. (Contributed by NM, 13-Oct-1997.)

Hypothesis

Ref	Expression
wcomcom.1	C (a, b) = 1

Assertion

Ref	Expression
wcomcom	C (b, a) = 1

Proof of Theorem wcomcom

Step	Hyp	Ref	Expression
1		cmtrcom 190	. 2 C (b, a) = C (a, b)
2		wcomcom.1	. 2 C (a, b) = 1
3	1, 2	ax-r2 36	1 C (b, a) = 1

Syntax hints:   = wb 1  1wt 8   C wcmtr 29

This theorem was proved from axioms:  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-cmtr 134

This theorem is referenced by:  wcomcom3  416  wcom3ii  419  wfh2  424  wcom2or  427  wnbdi  429  ska2  432  ska4  433  woml6  436