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Theorem nfcvf2 2655
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 2654 . 2  |-  ( -. 
A. y  y  =  x  ->  F/_ y x )
21naecoms 2026 1  |-  ( -. 
A. x  x  =  y  ->  F/_ y x )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377   F/_wnfc 2615
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-cleq 2459  df-clel 2462  df-nfc 2617
This theorem is referenced by:  dfid3  4796  oprabid  6309  axrepndlem1  8968  axrepndlem2  8969  axrepnd  8970  axunnd  8972  axpowndlem2OLD  8975  axpowndlem3  8976  axpowndlem3OLD  8977  axpowndlem4  8978  axpownd  8979  axregndlem2  8981  axinfndlem1  8984  axinfnd  8985  axacndlem4  8989  axacndlem5  8990  axacnd  8991  bj-nfcsym  33758
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