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Theorem nfint 4281
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 4273 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1712 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2840 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2620 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2614 1  |-  F/_ x |^| A
Colors of variables: wff setvar class
Syntax hints:   {cab 2439   F/_wnfc 2602   A.wral 2804   |^|cint 4271
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ral 2809  df-int 4272
This theorem is referenced by:  onminsb  6607  oawordeulem  7195  nnawordex  7278  rankidb  8209  cardmin2  8370  cardaleph  8461  cardmin  8930  sltval2  29656  nobndlem5  29696  aomclem8  31246
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