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Theorem nfin 3230
Description: Hypothesis builder for intersection. (Contributed by SF, 2-Jan-2018.)
Hypotheses
Ref Expression
nfbool.1 xA
nfbool.2 xB
Assertion
Ref Expression
nfin x(AB)

Proof of Theorem nfin
StepHypRef Expression
1 df-in 3213 . 2 (AB) = ∼ (AB)
2 nfbool.1 . . . 4 xA
3 nfbool.2 . . . 4 xB
42, 3nfnin 3228 . . 3 x(AB)
54nfcompl 3229 . 2 x ∼ (AB)
61, 5nfcxfr 2486 1 x(AB)
Colors of variables: wff setvar class
Syntax hints:  wnfc 2476  cnin 3204  ccompl 3205  cin 3208
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-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  df-compl 3212  df-in 3213
This theorem is referenced by:  nfdif  3232  csbing  3462  nfres  4936
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