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

Definition df-pt 14542
 Description: Define the product topology on a collection of topologies. For convenience, it is defined on arbitrary collections of sets, expressed as a function from some index set to the subbases of each factor space. (Contributed by Mario Carneiro, 3-Feb-2015.)
Assertion
Ref Expression
df-pt
Distinct variable group:   ,,,,

Detailed syntax breakdown of Definition df-pt
StepHypRef Expression
1 cpt 14536 . 2
2 vf . . 3
3 cvv 3081 . . 3
4 vg . . . . . . . . . 10
54cv 1369 . . . . . . . . 9
62cv 1369 . . . . . . . . . 10
76cdm 4957 . . . . . . . . 9
85, 7wfn 5532 . . . . . . . 8
9 vy . . . . . . . . . . . 12
109cv 1369 . . . . . . . . . . 11
1110, 5cfv 5537 . . . . . . . . . 10
1210, 6cfv 5537 . . . . . . . . . 10
1311, 12wcel 1758 . . . . . . . . 9
1413, 9, 7wral 2800 . . . . . . . 8
1512cuni 4208 . . . . . . . . . . 11
1611, 15wceq 1370 . . . . . . . . . 10
17 vz . . . . . . . . . . . 12
1817cv 1369 . . . . . . . . . . 11
197, 18cdif 3439 . . . . . . . . . 10
2016, 9, 19wral 2800 . . . . . . . . 9
21 cfn 7444 . . . . . . . . 9
2220, 17, 21wrex 2801 . . . . . . . 8
238, 14, 22w3a 965 . . . . . . 7
24 vx . . . . . . . . 9
2524cv 1369 . . . . . . . 8
269, 7, 11cixp 7397 . . . . . . . 8
2725, 26wceq 1370 . . . . . . 7
2823, 27wa 369 . . . . . 6
2928, 4wex 1587 . . . . 5
3029, 24cab 2439 . . . 4
31 ctg 14535 . . . 4
3230, 31cfv 5537 . . 3
332, 3, 32cmpt 4467 . 2
341, 33wceq 1370 1
 Colors of variables: wff setvar class This definition is referenced by:  ptval  19542
 Copyright terms: Public domain W3C validator