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Theorem nfint 3817
 Description: Bound-variable hypothesis builder for intersection. (Contributed by NM, 2-Feb-1997.) (Proof shortened by Andrew Salmon, 12-Aug-2011.)
Hypothesis
Ref Expression
nfint.1
Assertion
Ref Expression
nfint

Proof of Theorem nfint
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfint2 3809 . 2
2 nfint.1 . . . 4
3 nfv 1508 . . . 4
42, 3nfralxy 2495 . . 3
54nfab 2304 . 2
61, 5nfcxfr 2296 1
 Colors of variables: wff set class Syntax hints:  cab 2143  wnfc 2286  wral 2435  cint 3807 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-int 3808 This theorem is referenced by: (None)
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