Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-xmul Unicode version

Definition df-xmul 11349
 Description: Define multiplication over extended real numbers. (Contributed by Mario Carneiro, 20-Aug-2015.)
Assertion
Ref Expression
df-xmul
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-xmul
StepHypRef Expression
1 cxmu 11346 . 2
2 vx . . 3
3 vy . . 3
4 cxr 9648 . . 3
52cv 1394 . . . . . 6
6 cc0 9513 . . . . . 6
75, 6wceq 1395 . . . . 5
83cv 1394 . . . . . 6
98, 6wceq 1395 . . . . 5
107, 9wo 368 . . . 4
11 clt 9649 . . . . . . . . 9
126, 8, 11wbr 4452 . . . . . . . 8
13 cpnf 9646 . . . . . . . . 9
145, 13wceq 1395 . . . . . . . 8
1512, 14wa 369 . . . . . . 7
168, 6, 11wbr 4452 . . . . . . . 8
17 cmnf 9647 . . . . . . . . 9
185, 17wceq 1395 . . . . . . . 8
1916, 18wa 369 . . . . . . 7
2015, 19wo 368 . . . . . 6
216, 5, 11wbr 4452 . . . . . . . 8
228, 13wceq 1395 . . . . . . . 8
2321, 22wa 369 . . . . . . 7
245, 6, 11wbr 4452 . . . . . . . 8
258, 17wceq 1395 . . . . . . . 8
2624, 25wa 369 . . . . . . 7
2723, 26wo 368 . . . . . 6
2820, 27wo 368 . . . . 5
2912, 18wa 369 . . . . . . . 8
3016, 14wa 369 . . . . . . . 8
3129, 30wo 368 . . . . . . 7
3221, 25wa 369 . . . . . . . 8
3324, 22wa 369 . . . . . . . 8
3432, 33wo 368 . . . . . . 7
3531, 34wo 368 . . . . . 6
36 cmul 9518 . . . . . . 7
375, 8, 36co 6296 . . . . . 6
3835, 17, 37cif 3941 . . . . 5
3928, 13, 38cif 3941 . . . 4
4010, 6, 39cif 3941 . . 3
412, 3, 4, 4, 40cmpt2 6298 . 2
421, 41wceq 1395 1
 Colors of variables: wff setvar class This definition is referenced by:  xmulval  11453  xmulf  11493
 Copyright terms: Public domain W3C validator