Definition df-cmtr 134

Description: Define 'commutator'.

Assertion

Ref	Expression
df-cmtr	C (a, b) = (((a ^ b) v (a ^ b')) v ((a' ^ b) v (a' ^ b')))

Detailed syntax breakdown of Definition df-cmtr

Step	Hyp	Ref	Expression
1		wva	. . 3 term a
2		wvb	. . 3 term b
3	1, 2	wcmtr 29	. 2 term C (a, b)
4	1, 2	wa 7	. . . 4 term (a ^ b)
5	2	wn 4	. . . . 5 term b'
6	1, 5	wa 7	. . . 4 term (a ^ b')
7	4, 6	wo 6	. . 3 term ((a ^ b) v (a ^ b'))
8	1	wn 4	. . . . 5 term a'
9	8, 2	wa 7	. . . 4 term (a' ^ b)
10	8, 5	wa 7	. . . 4 term (a' ^ b')
11	9, 10	wo 6	. . 3 term ((a' ^ b) v (a' ^ b'))
12	7, 11	wo 6	. 2 term (((a ^ b) v (a ^ b')) v ((a' ^ b) v (a' ^ b')))
13	3, 12	wb 1	1 wff C (a, b) = (((a ^ b) v (a ^ b')) v ((a' ^ b) v (a' ^ b')))

This definition is referenced by:  cmtrcom 190  wdf-c1 383  wdf-c2 384  cmtr1com 493  comcmtr1 494  i0cmtrcom 495  3vded22 818  wdcom 1102  wdwom 1103

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