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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  |-  F/_ x A
Assertion
Ref Expression
nfint  |-  F/_ x |^| A

Proof of Theorem nfint
Dummy variables  y  z are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfint2 3645 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1437 . . . 4  |-  F/ x  y  e.  z
42, 3nfralxy 2377 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2198 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2191 1  |-  F/_ x |^| A
Colors of variables: wff set class
Syntax hints:   {cab 2042   F/_wnfc 2181   A.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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