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Axiom ax-cnv 4080
 Description: State the axiom of converse. This axiom guarantees the existence of the Kuratowski converse of x. Axiom P7 of [Hailperin] p. 10. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
ax-cnv yzw(⟪z, w y ↔ ⟪w, z x)
Distinct variable group:   x,y,z,w

Detailed syntax breakdown of Axiom ax-cnv
StepHypRef Expression
1 vz . . . . . . . 8 setvar z
21cv 1641 . . . . . . 7 class z
3 vw . . . . . . . 8 setvar w
43cv 1641 . . . . . . 7 class w
52, 4copk 4057 . . . . . 6 class z, w
6 vy . . . . . . 7 setvar y
76cv 1641 . . . . . 6 class y
85, 7wcel 1710 . . . . 5 wff z, w y
94, 2copk 4057 . . . . . 6 class w, z
10 vx . . . . . . 7 setvar x
1110cv 1641 . . . . . 6 class x
129, 11wcel 1710 . . . . 5 wff w, z x
138, 12wb 176 . . . 4 wff (⟪z, w y ↔ ⟪w, z x)
1413, 3wal 1540 . . 3 wff w(⟪z, w y ↔ ⟪w, z x)
1514, 1wal 1540 . 2 wff zw(⟪z, w y ↔ ⟪w, z x)
1615, 6wex 1541 1 wff yzw(⟪z, w y ↔ ⟪w, z x)
 Colors of variables: wff setvar class This axiom is referenced by:  axcnvprim  4091  cnvkexg  4286
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