New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  nineq12i Unicode version

Theorem nineq12i 3239
 Description: Equality inference for anti-intersection. (Contributed by SF, 11-Jan-2015.)
Hypotheses
Ref Expression
nineqi.1
nineq12i.2
Assertion
Ref Expression
nineq12i &ncap &ncap

Proof of Theorem nineq12i
StepHypRef Expression
1 nineqi.1 . 2
2 nineq12i.2 . 2
3 nineq12 3236 . 2 &ncap &ncap
41, 2, 3mp2an 653 1 &ncap &ncap
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   &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:  dfin5  3545
 Copyright terms: Public domain W3C validator