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Axiom ax-iinf 4338
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  |-  E. x
( (/)  e.  x  /\  A. y ( y  e.  x  ->  suc  y  e.  x ) )
Distinct variable group:    x, y

Detailed syntax breakdown of Axiom ax-iinf
StepHypRef Expression
1 c0 3251 . . . 4  class  (/)
2 vx . . . . 5  setvar  x
32cv 1258 . . . 4  class  x
41, 3wcel 1409 . . 3  wff  (/)  e.  x
5 vy . . . . . 6  setvar  y
65, 2wel 1410 . . . . 5  wff  y  e.  x
75cv 1258 . . . . . . 7  class  y
87csuc 4129 . . . . . 6  class  suc  y
98, 3wcel 1409 . . . . 5  wff  suc  y  e.  x
106, 9wi 4 . . . 4  wff  ( y  e.  x  ->  suc  y  e.  x )
1110, 5wal 1257 . . 3  wff  A. y
( y  e.  x  ->  suc  y  e.  x
)
124, 11wa 101 . 2  wff  ( (/)  e.  x  /\  A. y
( y  e.  x  ->  suc  y  e.  x
) )
1312, 2wex 1397 1  wff  E. x
( (/)  e.  x  /\  A. y ( y  e.  x  ->  suc  y  e.  x ) )
Colors of variables: wff set class
This axiom is referenced by:  zfinf2  4339
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