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Theorem inf2 7208
 Description: Variation of Axiom of Infinity. There exists a non-empty set that is a subset of its union (using zfinf 7224 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 7207 . 2
3 dfss2 3092 . . . . 5
4 eluni 3730 . . . . . . 7
54imbi2i 305 . . . . . 6
65albii 1554 . . . . 5
73, 6bitri 242 . . . 4
87anbi2i 678 . . 3
98exbii 1580 . 2
102, 9mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wi 6   wa 360  wal 1532  wex 1537   wcel 1621   wne 2412   wss 3078  c0 3362  cuni 3727 This theorem is referenced by:  axinf2  7225 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-v 2729  df-dif 3081  df-in 3085  df-ss 3089  df-nul 3363  df-uni 3728
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