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Theorem ineqri 3691
 Description: Inference from membership to intersection. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
ineqri.1
Assertion
Ref Expression
ineqri
Distinct variable groups:   ,   ,   ,

Proof of Theorem ineqri
StepHypRef Expression
1 elin 3686 . . 3
2 ineqri.1 . . 3
31, 2bitri 249 . 2
43eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  i^icin 3474 This theorem is referenced by:  inidm  3706  inass  3707  dfin2  3733  indi  3743  inab  3765  in0  3811  pwin  4789  dmres  5299  dfres3  29188  inixp  30219 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-v 3111  df-in 3482
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