Theorem wcomcom4 417

Description: Commutation equivalence. Kalmbach 83 p. 23. (Contributed by NM, 13-Oct-1997.)

Hypothesis

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

Assertion

Ref	Expression
wcomcom4	C (a⊥ , b⊥ ) = 1

Proof of Theorem wcomcom4

Step	Hyp	Ref	Expression
1		wcomcom.1	. . 3 C (a, b) = 1
2	1	wcomcom3 416	. 2 C (a⊥ , b) = 1
3	2	wcomcom2 415	1 C (a⊥ , b⊥ ) = 1

Syntax hints:   = wb 1  ^⊥ wn 4  1wt 8   C wcmtr 29

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-wom 361

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131  df-cmtr 134

This theorem is referenced by:  wcomd  418  wcomcom5  420  wfh3  425  wfh4  426  wcom2an  428  wlem14  430