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Theorem nfint 3653
 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 3645 . 2
2 nfint.1 . . . 4
3 nfv 1437 . . . 4
42, 3nfralxy 2377 . . 3
54nfab 2198 . 2
61, 5nfcxfr 2191 1
 Colors of variables: wff set class Syntax hints:  cab 2042  wnfc 2181  wral 2323  cint 3643 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-int 3644 This theorem is referenced by: (None)
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