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Axiom ax-cnv 3182
Description: State the axiom of converse. This axiom guarantees the existence of the Kuratowski converse of x. Axiom P7 of {{Hailperin}}.
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 set z
21cv 1397 . . . . . . 7 class z
3 vw . . . . . . . 8 set w
43cv 1397 . . . . . . 7 class w
52, 4copk 2862 . . . . . 6 class z, w
6 vy . . . . . . 7 set y
76cv 1397 . . . . . 6 class y
85, 7wcel 1400 . . . . 5 wff z, w y
94, 2copk 2862 . . . . . 6 class w, z
10 vx . . . . . . 7 set x
1110cv 1397 . . . . . 6 class x
129, 11wcel 1400 . . . . 5 wff w, z x
138, 12wb 173 . . . 4 wff (⟪z, w y ↔ ⟪w, z x)
1413, 3wal 1322 . . 3 wff w(⟪z, w y ↔ ⟪w, z x)
1514, 1wal 1322 . 2 wff zw(⟪z, w y ↔ ⟪w, z x)
1615, 6wex 1327 1 wff yzw(⟪z, w y ↔ ⟪w, z x)
Colors of variables: wff set class
This axiom is referenced by:  axcnvprim  3193  cnvkexg  3390
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