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

Definition df-xps 13724
 Description: Define a binary product on structures. (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
df-xps s s Scalars
Distinct variable group:   ,,,

Detailed syntax breakdown of Definition df-xps
StepHypRef Expression
1 cxps 13720 . 2 s
2 vr . . 3
3 vs . . 3
4 cvv 2948 . . 3
5 vx . . . . . 6
6 vy . . . . . 6
72cv 1651 . . . . . . 7
8 cbs 13457 . . . . . . 7
97, 8cfv 5445 . . . . . 6
103cv 1651 . . . . . . 7
1110, 8cfv 5445 . . . . . 6
125cv 1651 . . . . . . . . 9
1312csn 3806 . . . . . . . 8
146cv 1651 . . . . . . . . 9
1514csn 3806 . . . . . . . 8
16 ccda 8036 . . . . . . . 8
1713, 15, 16co 6072 . . . . . . 7
1817ccnv 4868 . . . . . 6
195, 6, 9, 11, 18cmpt2 6074 . . . . 5
2019ccnv 4868 . . . 4
21 csca 13520 . . . . . 6 Scalar
227, 21cfv 5445 . . . . 5 Scalar
237csn 3806 . . . . . . 7
2410csn 3806 . . . . . . 7
2523, 24, 16co 6072 . . . . . 6
2625ccnv 4868 . . . . 5
27 cprds 13657 . . . . 5 s
2822, 26, 27co 6072 . . . 4 Scalars
29 cimas 13718 . . . 4 s
3020, 28, 29co 6072 . . 3 s Scalars
312, 3, 4, 4, 30cmpt2 6074 . 2 s Scalars
321, 31wceq 1652 1 s s Scalars
 Colors of variables: wff set class This definition is referenced by:  xpsval  13785
 Copyright terms: Public domain W3C validator