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Axiom ax-typlower 3188
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}}.
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 1401 . . . 4 wff z y
4 vw . . . . . . . 8 set w
54cv 1397 . . . . . . 7 class w
61cv 1397 . . . . . . . 8 class z
76csn 2803 . . . . . . 7 class {z}
85, 7copk 2862 . . . . . 6 class w, {z}⟫
9 vx . . . . . . 7 set x
109cv 1397 . . . . . 6 class x
118, 10wcel 1400 . . . . 5 wff w, {z}⟫ x
1211, 4wal 1322 . . . 4 wff ww, {z}⟫ x
133, 12wb 173 . . 3 wff (z yww, {z}⟫ x)
1413, 1wal 1322 . 2 wff z(z yww, {z}⟫ x)
1514, 2wex 1327 1 wff yz(z yww, {z}⟫ x)
Colors of variables: wff set class
This axiom is referenced by:  axtyplowerprim  3196  p6exg  3394
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