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Theorem nineq1 3234
 Description: Equality law for anti-intersection. (Contributed by SF, 11-Jan-2015.)
Assertion
Ref Expression
nineq1 &ncap &ncap

Proof of Theorem nineq1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2414 . . . 4
21nanbi1d 1301 . . 3
32abbidv 2467 . 2
4 df-nin 3211 . 2 &ncap
5 df-nin 3211 . 2 &ncap
63, 4, 53eqtr4g 2410 1 &ncap &ncap
 Colors of variables: wff setvar class Syntax hints:   wi 4   wnan 1287   wceq 1642   wcel 1710  cab 2339   &ncap cnin 3204 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-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-nin 3211 This theorem is referenced by:  nineq2  3235  nineq12  3236  nineq1i  3237  nineq1d  3240  difeq1  3246  ninexg  4097
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