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Definition df-ins3k 4188
 Description: Define the Kuratowski third insertion operator. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-ins3k Ins3k A = {x yz(x = ⟪y, z tuv(y = {{t}} z = ⟪u, vt, u A))}
Distinct variable group:   x,A,y,z,t,u,v

Detailed syntax breakdown of Definition df-ins3k
StepHypRef Expression
1 cA . . 3 class A
21cins3k 4177 . 2 class Ins3k 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 . . . . . . . . . . . . . 14 setvar t
1211cv 1641 . . . . . . . . . . . . 13 class t
1312csn 3737 . . . . . . . . . . . 12 class {t}
1413csn 3737 . . . . . . . . . . 11 class {{t}}
156, 14wceq 1642 . . . . . . . . . 10 wff y = {{t}}
16 vu . . . . . . . . . . . . 13 setvar u
1716cv 1641 . . . . . . . . . . . 12 class u
18 vv . . . . . . . . . . . . 13 setvar v
1918cv 1641 . . . . . . . . . . . 12 class v
2017, 19copk 4057 . . . . . . . . . . 11 class u, v
218, 20wceq 1642 . . . . . . . . . 10 wff z = ⟪u, v
2212, 17copk 4057 . . . . . . . . . . 11 class t, u
2322, 1wcel 1710 . . . . . . . . . 10 wff t, u A
2415, 21, 23w3a 934 . . . . . . . . 9 wff (y = {{t}} z = ⟪u, vt, u A)
2524, 18wex 1541 . . . . . . . 8 wff v(y = {{t}} z = ⟪u, vt, u A)
2625, 16wex 1541 . . . . . . 7 wff uv(y = {{t}} z = ⟪u, vt, u A)
2726, 11wex 1541 . . . . . 6 wff tuv(y = {{t}} z = ⟪u, vt, u A)
2810, 27wa 358 . . . . 5 wff (x = ⟪y, z tuv(y = {{t}} z = ⟪u, vt, u A))
2928, 7wex 1541 . . . 4 wff z(x = ⟪y, z tuv(y = {{t}} z = ⟪u, vt, u A))
3029, 5wex 1541 . . 3 wff yz(x = ⟪y, z tuv(y = {{t}} z = ⟪u, vt, u A))
3130, 3cab 2339 . 2 class {x yz(x = ⟪y, z tuv(y = {{t}} z = ⟪u, vt, u A))}
322, 31wceq 1642 1 wff Ins3k A = {x yz(x = ⟪y, z tuv(y = {{t}} z = ⟪u, vt, u A))}
 Colors of variables: wff setvar class This definition is referenced by:  ins3keq  4219  opkelins3kg  4252  ins3kss  4280
 Copyright terms: Public domain W3C validator