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Axiom ax-sset 4082
Description: State the axiom of the subset relationship. This axiom guarantees the existence of the Kuratowski relationship representing subset. Slight generalization of axiom P9 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
ax-sset xyz(⟪y, z xw(w yw z))
Distinct variable group:   x,y,z,w

Detailed syntax breakdown of Axiom ax-sset
StepHypRef Expression
1 vy . . . . . . . 8 set y
21cv 1641 . . . . . . 7 class y
3 vz . . . . . . . 8 set z
43cv 1641 . . . . . . 7 class z
52, 4copk 4057 . . . . . 6 class y, z
6 vx . . . . . . 7 set x
76cv 1641 . . . . . 6 class x
85, 7wcel 1710 . . . . 5 wff y, z x
9 vw . . . . . . . 8 set w
109, 1wel 1711 . . . . . . 7 wff w y
119, 3wel 1711 . . . . . . 7 wff w z
1210, 11wi 4 . . . . . 6 wff (w yw z)
1312, 9wal 1540 . . . . 5 wff w(w yw z)
148, 13wb 176 . . . 4 wff (⟪y, z xw(w yw z))
1514, 3wal 1540 . . 3 wff z(⟪y, z xw(w yw z))
1615, 1wal 1540 . 2 wff yz(⟪y, z xw(w yw z))
1716, 6wex 1541 1 wff xyz(⟪y, z xw(w yw z))
Colors of variables: wff set class
This axiom is referenced by:  axssetprim  4092  ssetkex  4294
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