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Theorem inf2 8061
 Description: Variation of Axiom of Infinity. There exists a nonempty set that is a subset of its union (using zfinf 8077 as a hypothesis). Abbreviated version of the Axiom of Infinity in [FreydScedrov] p. 283. (Contributed by NM, 28-Oct-1996.)
Hypothesis
Ref Expression
inf1.1
Assertion
Ref Expression
inf2
Distinct variable group:   ,,

Proof of Theorem inf2
StepHypRef Expression
1 inf1.1 . . 3
21inf1 8060 . 2
3 dfss2 3492 . . . . 5
4 eluni 4252 . . . . . . 7
54imbi2i 312 . . . . . 6
65albii 1640 . . . . 5
73, 6bitri 249 . . . 4
87anbi2i 694 . . 3
98exbii 1667 . 2
102, 9mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  e.wcel 1818  =/=wne 2652  C_wss 3475   c0 3784  U.cuni 4249 This theorem is referenced by:  axinf2  8078 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-uni 4250
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