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Theorem zfinf 8077
 Description: Axiom of Infinity expressed with the fewest number of different variables. (New usage is discouraged.) (Contributed by NM, 14-Aug-2003.)
Assertion
Ref Expression
zfinf
Distinct variable group:   ,,

Proof of Theorem zfinf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-inf 8076 . 2
2 elequ1 1821 . . . . . 6
3 elequ1 1821 . . . . . . . 8
43anbi1d 704 . . . . . . 7
54exbidv 1714 . . . . . 6
62, 5imbi12d 320 . . . . 5
76cbvalv 2023 . . . 4
87anbi2i 694 . . 3
98exbii 1667 . 2
101, 9mpbi 208 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612 This theorem is referenced by:  axinf2  8078  axinfndlem1  9004 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-inf 8076 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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