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Axiom ax-iinf 4207
Description: Axiom of Infinity. Axiom 5 of [Crosilla] p. "Axioms of CZF and IZF". (Contributed by Jim Kingdon, 16-Nov-2018.)
Assertion
Ref Expression
ax-iinf x(∅ x y(y x → suc y x))
Distinct variable group:   x,y

Detailed syntax breakdown of Axiom ax-iinf
StepHypRef Expression
1 c0 3202 . . . 4 class
2 vx . . . . 5 setvar x
32cv 1372 . . . 4 class x
41, 3wcel 1375 . . 3 wff x
5 vy . . . . . 6 setvar y
65, 2wel 1376 . . . . 5 wff y x
75cv 1372 . . . . . . 7 class y
87csuc 4026 . . . . . 6 class suc y
98, 3wcel 1375 . . . . 5 wff suc y x
106, 9wi 4 . . . 4 wff (y x → suc y x)
1110, 5wal 1314 . . 3 wff y(y x → suc y x)
124, 11wa 97 . 2 wff (∅ x y(y x → suc y x))
1312, 2wex 1361 1 wff x(∅ x y(y x → suc y x))
Colors of variables: wff set class
This axiom is referenced by:  zfinf2  4208
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