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Theorem ineqri 3633
 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 3626 . . 3
2 ineqri.1 . . 3
31, 2bitri 249 . 2
43eqriv 2398 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 367   wceq 1405   wcel 1842   cin 3413 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3061  df-in 3421 This theorem is referenced by:  inidm  3648  inass  3649  dfin2  3686  indi  3696  inab  3718  in0  3765  pwin  4727  dmres  5114  dfres3  29972  inixp  31501
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