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Theorem ineqri 3194
 Description: Inference from membership to intersection. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
ineqri.1
Assertion
Ref Expression
ineqri
Distinct variable groups:   ,   ,   ,

Proof of Theorem ineqri
StepHypRef Expression
1 elin 3184 . . 3
2 ineqri.1 . . 3
31, 2bitri 183 . 2
43eqriv 2086 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104   wceq 1290   wcel 1439   cin 2999 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-in 3006 This theorem is referenced by:  inidm  3210  inass  3211  indi  3247  inab  3268  in0  3321  pwin  4118  dmres  4747
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