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Axiom ax-ins3 4085
 Description: State the insertion three axiom. This axiom sets up a set that inserts an extra variable at the third place of the relationship described by x. Axiom P4 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
ax-ins3 yzwt(⟪{{z}}, ⟪w, t⟫⟫ y ↔ ⟪z, w x)
Distinct variable group:   x,y,z,w,t

Detailed syntax breakdown of Axiom ax-ins3
StepHypRef Expression
1 vz . . . . . . . . . . 11 setvar z
21cv 1641 . . . . . . . . . 10 class z
32csn 3737 . . . . . . . . 9 class {z}
43csn 3737 . . . . . . . 8 class {{z}}
5 vw . . . . . . . . . 10 setvar w
65cv 1641 . . . . . . . . 9 class w
7 vt . . . . . . . . . 10 setvar t
87cv 1641 . . . . . . . . 9 class t
96, 8copk 4057 . . . . . . . 8 class w, t
104, 9copk 4057 . . . . . . 7 class ⟪{{z}}, ⟪w, t⟫⟫
11 vy . . . . . . . 8 setvar y
1211cv 1641 . . . . . . 7 class y
1310, 12wcel 1710 . . . . . 6 wff ⟪{{z}}, ⟪w, t⟫⟫ y
142, 6copk 4057 . . . . . . 7 class z, w
15 vx . . . . . . . 8 setvar x
1615cv 1641 . . . . . . 7 class x
1714, 16wcel 1710 . . . . . 6 wff z, w x
1813, 17wb 176 . . . . 5 wff (⟪{{z}}, ⟪w, t⟫⟫ y ↔ ⟪z, w x)
1918, 7wal 1540 . . . 4 wff t(⟪{{z}}, ⟪w, t⟫⟫ y ↔ ⟪z, w x)
2019, 5wal 1540 . . 3 wff wt(⟪{{z}}, ⟪w, t⟫⟫ y ↔ ⟪z, w x)
2120, 1wal 1540 . 2 wff zwt(⟪{{z}}, ⟪w, t⟫⟫ y ↔ ⟪z, w x)
2221, 11wex 1541 1 wff yzwt(⟪{{z}}, ⟪w, t⟫⟫ y ↔ ⟪z, w x)
 Colors of variables: wff setvar class This axiom is referenced by:  axins3prim  4096  ins3kexg  4306
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