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Axiom ax-infvn 9375
Description: Axiom of infinity in a constructive setting. This asserts the existence of the special set we want (the set of natural numbers), instead of the existence of a set with some properties (ax-iinf 4254) from which one then proves (omex 4259) using full separation that the wanted set exists. "vn" is for "Von Neumann". (Contributed by BJ, 14-Nov-2019.)
Assertion
Ref Expression
ax-infvn x(Ind x y(Ind yxy))
Distinct variable group:   x,y

Detailed syntax breakdown of Axiom ax-infvn
StepHypRef Expression
1 vx . . . . 5 setvar x
21cv 1241 . . . 4 class x
32wind 9361 . . 3 wff Ind x
4 vy . . . . . . 7 setvar y
54cv 1241 . . . . . 6 class y
65wind 9361 . . . . 5 wff Ind y
72, 5wss 2911 . . . . 5 wff xy
86, 7wi 4 . . . 4 wff (Ind yxy)
98, 4wal 1240 . . 3 wff y(Ind yxy)
103, 9wa 97 . 2 wff (Ind x y(Ind yxy))
1110, 1wex 1378 1 wff x(Ind x y(Ind yxy))
Colors of variables: wff set class
This axiom is referenced by:  bj-omex  9376
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