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Theorem nfint 3872
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 3864 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1605 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2596 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2423 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2416 1  |-  F/_ x |^| A
Colors of variables: wff set class
Syntax hints:    e. wcel 1684   {cab 2269   F/_wnfc 2406   A.wral 2543   |^|cint 3862
This theorem is referenced by:  onminsb  4590  oawordeulem  6552  nnawordex  6635  rankidb  7472  cardmin2  7631  cardaleph  7716  cardmin  8186  sltval2  24310  nobndlem5  24350  aomclem8  27159
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-int 3863
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