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Theorem intmin2 3641
 Description: Any set is the smallest of all sets that include it. (Contributed by NM, 20-Sep-2003.)
Hypothesis
Ref Expression
intmin2.1
Assertion
Ref Expression
intmin2
Distinct variable group:   ,

Proof of Theorem intmin2
StepHypRef Expression
1 rabab 2575 . . 3
21inteqi 3619 . 2
3 intmin2.1 . . 3
4 intmin 3635 . . 3
53, 4ax-mp 7 . 2
62, 5eqtr3i 2062 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   wcel 1393  cab 2026  crab 2310  cvv 2557   wss 2917  cint 3615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rab 2315  df-v 2559  df-in 2924  df-ss 2931  df-int 3616 This theorem is referenced by: (None)
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