Theorem wcomcom3 398

Description: Commutation equivalence. Kalmbach 83 p. 23.

Hypothesis

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

Assertion

Ref	Expression
wcomcom3	C (a⊥ , b) = 1

Proof of Theorem wcomcom3

Step	Hyp	Ref	Expression
1		wcomcom.1	. . . 4 C (a, b) = 1
2	1	wcomcom 396	. . 3 C (b, a) = 1
3	2	wcomcom2 397	. 2 C (b, a⊥ ) = 1
4	3	wcomcom 396	1 C (a⊥ , b) = 1

Syntax hints:   = wb 1  ^⊥ wn 4  1wt 9   C wcmtr 28

This theorem is referenced by:  wcomcom4 399  wfh2 406  wcom2or 409  wlem14 412  ska2 414  woml6 418  woml7 419

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-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le 121  df-le1 122  df-le2 123  df-cmtr 126

metamath.org