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Theorem nfint 4052
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 4044 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1629 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2751 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2575 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2568 1  |-  F/_ x |^| A
Colors of variables: wff set class
Syntax hints:   {cab 2421   F/_wnfc 2558   A.wral 2697   |^|cint 4042
This theorem is referenced by:  onminsb  4771  oawordeulem  6789  nnawordex  6872  rankidb  7718  cardmin2  7877  cardaleph  7962  cardmin  8431  sltval2  25603  nobndlem5  25643  aomclem8  27127
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-int 4043
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