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Theorem nfcvf2 2455
Description: If  x and  y are distinct, then  y is not free in 
x. (Contributed by Mario Carneiro, 5-Dec-2016.)
Assertion
Ref Expression
nfcvf2  |-  ( -. 
A. x  x  =  y  ->  F/_ y x )

Proof of Theorem nfcvf2
StepHypRef Expression
1 nfcvf 2454 . 2  |-  ( -. 
A. y  y  =  x  ->  F/_ y x )
21naecoms 1901 1  |-  ( -. 
A. x  x  =  y  ->  F/_ y x )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   F/_wnfc 2419
This theorem is referenced by:  dfid3  4326  oprabid  5898  axrepndlem1  8230  axrepndlem2  8231  axrepnd  8232  axunnd  8234  axpowndlem2  8236  axpowndlem3  8237  axpowndlem4  8238  axpownd  8239  axregndlem2  8241  axinfndlem1  8243  axinfnd  8244  axacndlem4  8248  axacndlem5  8249  axacnd  8250
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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