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Axiom ax-xp 3181
Description: State the axiom of cross product. This axiom guarantees the existence of the (Kuratowski) cross product of V with x. Axiom P5 of {{Hailperin}}.
Assertion
Ref Expression
ax-xp yz(z ywt(z = ⟪w, t t x))
Distinct variable group:   x,y,z,w,t

Detailed syntax breakdown of Axiom ax-xp
StepHypRef Expression
1 vz . . . . 5 set z
2 vy . . . . 5 set y
31, 2wel 1401 . . . 4 wff z y
41cv 1397 . . . . . . . 8 class z
5 vw . . . . . . . . . 10 set w
65cv 1397 . . . . . . . . 9 class w
7 vt . . . . . . . . . 10 set t
87cv 1397 . . . . . . . . 9 class t
96, 8copk 2862 . . . . . . . 8 class w, t
104, 9wceq 1398 . . . . . . 7 wff z = ⟪w, t
11 vx . . . . . . . 8 set x
127, 11wel 1401 . . . . . . 7 wff t x
1310, 12wa 355 . . . . . 6 wff (z = ⟪w, t t x)
1413, 7wex 1327 . . . . 5 wff t(z = ⟪w, t t x)
1514, 5wex 1327 . . . 4 wff wt(z = ⟪w, t t x)
163, 15wb 173 . . 3 wff (z ywt(z = ⟪w, t t x))
1716, 1wal 1322 . 2 wff z(z ywt(z = ⟪w, t t x))
1817, 2wex 1327 1 wff yz(z ywt(z = ⟪w, t t x))
Colors of variables: wff set class
This axiom is referenced by:  axxpprim  3192  xpkvexg  3389
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