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Theorem nfint 4213
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 4205 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1764 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2769 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2596 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2590 1  |-  F/_ x |^| A
Colors of variables: wff setvar class
Syntax hints:   {cab 2437   F/_wnfc 2579   A.wral 2736   |^|cint 4203
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1672  ax-4 1685  ax-5 1761  ax-6 1808  ax-7 1854  ax-10 1918  ax-11 1923  ax-12 1936  ax-13 2091  ax-ext 2431
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1450  df-ex 1667  df-nf 1671  df-sb 1801  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2741  df-int 4204
This theorem is referenced by:  onminsb  6613  oawordeulem  7241  nnawordex  7324  rankidb  8257  cardmin2  8418  cardaleph  8506  cardmin  8975  ldsysgenld  28988  sltval2  30548  nobndlem5  30590  aomclem8  35920
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