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Theorem intmin3 3642
 Description: Under subset ordering, the intersection of a class abstraction is less than or equal to any of its members. (Contributed by NM, 3-Jul-2005.)
Hypotheses
Ref Expression
intmin3.2
intmin3.3
Assertion
Ref Expression
intmin3
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem intmin3
StepHypRef Expression
1 intmin3.3 . . 3
2 intmin3.2 . . . 4
32elabg 2688 . . 3
41, 3mpbiri 157 . 2
5 intss1 3630 . 2
64, 5syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243   wcel 1393  cab 2026   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-v 2559  df-in 2924  df-ss 2931  df-int 3616 This theorem is referenced by:  intid  3960
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