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Definition df-sik 4192
 Description: Define the Kuratowski singleton image operation. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-sik SIk A = {x yz(x = ⟪y, z tu(y = {t} z = {u} t, u A))}
Distinct variable group:   x,A,y,z,t,u

Detailed syntax breakdown of Definition df-sik
StepHypRef Expression
1 cA . . 3 class A
21csik 4181 . 2 class SIk A
3 vx . . . . . . . 8 setvar x
43cv 1641 . . . . . . 7 class x
5 vy . . . . . . . . 9 setvar y
65cv 1641 . . . . . . . 8 class y
7 vz . . . . . . . . 9 setvar z
87cv 1641 . . . . . . . 8 class z
96, 8copk 4057 . . . . . . 7 class y, z
104, 9wceq 1642 . . . . . 6 wff x = ⟪y, z
11 vt . . . . . . . . . . . 12 setvar t
1211cv 1641 . . . . . . . . . . 11 class t
1312csn 3737 . . . . . . . . . 10 class {t}
146, 13wceq 1642 . . . . . . . . 9 wff y = {t}
15 vu . . . . . . . . . . . 12 setvar u
1615cv 1641 . . . . . . . . . . 11 class u
1716csn 3737 . . . . . . . . . 10 class {u}
188, 17wceq 1642 . . . . . . . . 9 wff z = {u}
1912, 16copk 4057 . . . . . . . . . 10 class t, u
2019, 1wcel 1710 . . . . . . . . 9 wff t, u A
2114, 18, 20w3a 934 . . . . . . . 8 wff (y = {t} z = {u} t, u A)
2221, 15wex 1541 . . . . . . 7 wff u(y = {t} z = {u} t, u A)
2322, 11wex 1541 . . . . . 6 wff tu(y = {t} z = {u} t, u A)
2410, 23wa 358 . . . . 5 wff (x = ⟪y, z tu(y = {t} z = {u} t, u A))
2524, 7wex 1541 . . . 4 wff z(x = ⟪y, z tu(y = {t} z = {u} t, u A))
2625, 5wex 1541 . . 3 wff yz(x = ⟪y, z tu(y = {t} z = {u} t, u A))
2726, 3cab 2339 . 2 class {x yz(x = ⟪y, z tu(y = {t} z = {u} t, u A))}
282, 27wceq 1642 1 wff SIk A = {x yz(x = ⟪y, z tu(y = {t} z = {u} t, u A))}
 Colors of variables: wff setvar class This definition is referenced by:  sikeq  4241  opkelsikg  4264  sikssvvk  4266  sikss1c1c  4267
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