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Theorem ninex 4098
 Description: The anti-intersection of two sets is a set. (Contributed by SF, 12-Jan-2015.)
Hypotheses
Ref Expression
ninex.1 A V
ninex.2 B V
Assertion
Ref Expression
ninex (AB) V

Proof of Theorem ninex
StepHypRef Expression
1 ninex.1 . 2 A V
2 ninex.2 . 2 B V
3 ninexg 4097 . 2 ((A V B V) → (AB) V)
41, 2, 3mp2an 653 1 (AB) V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  Vcvv 2859   ⩃ 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  ax-nin 4078 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: (None)
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