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Definition df-xpk 4185
 Description: Define the Kuratowski cross product. This definition through df-idk 4195 set up the Kuratowski relationships. These are used mainly to prove the properties of df-op 4566, and are not used thereafter. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
df-xpk (A ×k B) = {x yz(x = ⟪y, z (y A z B))}
Distinct variable groups:   x,A,y,z   x,B,y,z

Detailed syntax breakdown of Definition df-xpk
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2cxpk 4174 . 2 class (A ×k B)
4 vx . . . . . . . 8 setvar x
54cv 1641 . . . . . . 7 class x
6 vy . . . . . . . . 9 setvar y
76cv 1641 . . . . . . . 8 class y
8 vz . . . . . . . . 9 setvar z
98cv 1641 . . . . . . . 8 class z
107, 9copk 4057 . . . . . . 7 class y, z
115, 10wceq 1642 . . . . . 6 wff x = ⟪y, z
127, 1wcel 1710 . . . . . . 7 wff y A
139, 2wcel 1710 . . . . . . 7 wff z B
1412, 13wa 358 . . . . . 6 wff (y A z B)
1511, 14wa 358 . . . . 5 wff (x = ⟪y, z (y A z B))
1615, 8wex 1541 . . . 4 wff z(x = ⟪y, z (y A z B))
1716, 6wex 1541 . . 3 wff yz(x = ⟪y, z (y A z B))
1817, 4cab 2339 . 2 class {x yz(x = ⟪y, z (y A z B))}
193, 18wceq 1642 1 wff (A ×k B) = {x yz(x = ⟪y, z (y A z B))}
 Colors of variables: wff setvar class This definition is referenced by:  elxpk  4196  xpkssvvk  4210  opkelxpkg  4247
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