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Axiom ax-typlower 4086
Description: The type lowering axiom. This axiom eventually sets up both the existence of the sum set and the existence of the range of a relationship. Axiom P6 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
ax-typlower yz(z yww, {z}⟫ x)
Distinct variable group:   x,y,z,w

Detailed syntax breakdown of Axiom ax-typlower
StepHypRef Expression
1 vz . . . . 5 set z
2 vy . . . . 5 set y
31, 2wel 1711 . . . 4 wff z y
4 vw . . . . . . . 8 set w
54cv 1641 . . . . . . 7 class w
61cv 1641 . . . . . . . 8 class z
76csn 3737 . . . . . . 7 class {z}
85, 7copk 4057 . . . . . 6 class w, {z}⟫
9 vx . . . . . . 7 set x
109cv 1641 . . . . . 6 class x
118, 10wcel 1710 . . . . 5 wff w, {z}⟫ x
1211, 4wal 1540 . . . 4 wff ww, {z}⟫ x
133, 12wb 176 . . 3 wff (z yww, {z}⟫ x)
1413, 1wal 1540 . 2 wff z(z yww, {z}⟫ x)
1514, 2wex 1541 1 wff yz(z yww, {z}⟫ x)
Colors of variables: wff set class
This axiom is referenced by:  axtyplowerprim  4094  p6exg  4290
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