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Theorem nfnin 3228
 Description: Hypothesis builder for anti-intersection. (Contributed by SF, 2-Jan-2018.)
Hypotheses
Ref Expression
nfnin.1 xA
nfnin.2 xB
Assertion
Ref Expression
nfnin x(AB)

Proof of Theorem nfnin
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-nin 3211 . 2 (AB) = {y (y A y B)}
2 nfnin.1 . . . . 5 xA
32nfel2 2501 . . . 4 x y A
4 nfnin.2 . . . . 5 xB
54nfel2 2501 . . . 4 x y B
63, 5nfnan 1825 . . 3 x(y A y B)
76nfab 2493 . 2 x{y (y A y B)}
81, 7nfcxfr 2486 1 x(AB)
 Colors of variables: wff setvar class Syntax hints:   ⊼ wnan 1287   ∈ wcel 1710  {cab 2339  Ⅎwnfc 2476   ⩃ 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-nin 3211 This theorem is referenced by:  nfcompl  3229  nfin  3230  nfun  3231
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