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Theorem nfcvf 2199
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 2178 . 2  |-  F/_ x
z
2 nfcv 2178 . 2  |-  F/_ z
y
3 id 19 . 2  |-  ( z  =  y  ->  z  =  y )
41, 2, 3dvelimc 2198 1  |-  ( -. 
A. x  x  =  y  ->  F/_ x y )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1241   F/_wnfc 2165
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167
This theorem is referenced by:  nfcvf2  2200
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