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Theorem nfcvf 2454
Description: If  x and  y are distinct, then  x is not free in  y. (Contributed by Mario Carneiro, 8-Oct-2016.)
Assertion
Ref Expression
nfcvf  |-  ( -. 
A. x  x  =  y  ->  F/_ x y )

Proof of Theorem nfcvf
Dummy variable  z is distinct from all other variables.
StepHypRef Expression
1 nfcv 2432 . 2  |-  F/_ x
z
2 nfcv 2432 . 2  |-  F/_ z
y
3 id 19 . 2  |-  ( z  =  y  ->  z  =  y )
41, 2, 3dvelimc 2453 1  |-  ( -. 
A. x  x  =  y  ->  F/_ x y )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530    = wceq 1632   F/_wnfc 2419
This theorem is referenced by:  nfcvf2  2455  nfrald  2607  ralcom2  2717  nfreud  2725  nfrmod  2726  nfrmo  2728  nfdisj  4021  nfcvb  4221  nfiotad  5238  nfriotad  6329  nfixp  6851  axextnd  8229  axrepndlem1  8230  axrepndlem2  8231  axrepnd  8232  axunndlem1  8233  axunnd  8234  axpowndlem2  8236  axpowndlem4  8238  axregndlem2  8241  axregnd  8242  axinfndlem1  8243  axinfnd  8244  axacndlem4  8248  axacndlem5  8249  axacnd  8250  axextdist  24227
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-cleq 2289  df-clel 2292  df-nfc 2421
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