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Theorem nfint 3888
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 3880 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1609 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2609 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2436 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2429 1  |-  F/_ x |^| A
Colors of variables: wff set class
Syntax hints:    e. wcel 1696   {cab 2282   F/_wnfc 2419   A.wral 2556   |^|cint 3878
This theorem is referenced by:  onminsb  4606  oawordeulem  6568  nnawordex  6651  rankidb  7488  cardmin2  7647  cardaleph  7732  cardmin  8202  sltval2  24381  nobndlem5  24421  aomclem8  27262
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-int 3879
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