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Definition df-con 20967
Description: Topologies are connected when only and 𝑗 are both open and closed. (Contributed by FL, 17-Nov-2008.)
Assertion
Ref Expression
df-con Con = {𝑗 ∈ Top ∣ (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}}

Detailed syntax breakdown of Definition df-con
StepHypRef Expression
1 ccon 20966 . 2 class Con
2 vj . . . . . 6 setvar 𝑗
32cv 1473 . . . . 5 class 𝑗
4 ccld 20572 . . . . . 6 class Clsd
53, 4cfv 5790 . . . . 5 class (Clsd‘𝑗)
63, 5cin 3538 . . . 4 class (𝑗 ∩ (Clsd‘𝑗))
7 c0 3873 . . . . 5 class
83cuni 4366 . . . . 5 class 𝑗
97, 8cpr 4126 . . . 4 class {∅, 𝑗}
106, 9wceq 1474 . . 3 wff (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}
11 ctop 20459 . . 3 class Top
1210, 2, 11crab 2899 . 2 class {𝑗 ∈ Top ∣ (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}}
131, 12wceq 1474 1 wff Con = {𝑗 ∈ Top ∣ (𝑗 ∩ (Clsd‘𝑗)) = {∅, 𝑗}}
Colors of variables: wff setvar class
This definition is referenced by:  iscon  20968
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