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Theorem elnin 3224
 Description: Membership in anti-intersection. (Contributed by SF, 10-Jan-2015.)
Hypothesis
Ref Expression
elbool.1
Assertion
Ref Expression
elnin &ncap

Proof of Theorem elnin
StepHypRef Expression
1 elbool.1 . 2
2 elning 3217 . 2 &ncap
31, 2ax-mp 8 1 &ncap
 Colors of variables: wff setvar class Syntax hints:   wb 176   wnan 1287   wcel 1710  cvv 2859   &ncap cnin 3204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211 This theorem is referenced by:  nincom  3226  nincompl  4072  ninexg  4097
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