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Theorem nfint 4292
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 4284 . 2  |-  |^| A  =  { y  |  A. z  e.  A  y  e.  z }
2 nfint.1 . . . 4  |-  F/_ x A
3 nfv 1683 . . . 4  |-  F/ x  y  e.  z
42, 3nfral 2850 . . 3  |-  F/ x A. z  e.  A  y  e.  z
54nfab 2633 . 2  |-  F/_ x { y  |  A. z  e.  A  y  e.  z }
61, 5nfcxfr 2627 1  |-  F/_ x |^| A
Colors of variables: wff setvar class
Syntax hints:   {cab 2452   F/_wnfc 2615   A.wral 2814   |^|cint 4282
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-int 4283
This theorem is referenced by:  onminsb  6619  oawordeulem  7204  nnawordex  7287  rankidb  8219  cardmin2  8380  cardaleph  8471  cardmin  8940  sltval2  29269  nobndlem5  29309  aomclem8  30838
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