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Theorem nfint 4003
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 3995 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1626 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2703 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2528 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2521 1  |-  F/_ x |^| A
Colors of variables: wff set class
Syntax hints:   {cab 2374   F/_wnfc 2511   A.wral 2650   |^|cint 3993
This theorem is referenced by:  onminsb  4720  oawordeulem  6734  nnawordex  6817  rankidb  7660  cardmin2  7819  cardaleph  7904  cardmin  8373  sltval2  25335  nobndlem5  25375  aomclem8  26829
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-ral 2655  df-int 3994
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