Theorem nfcvf2 2200

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

Step	Hyp	Ref	Expression
1		nfcvf 2199	. 2 |- ( -. A. y y = x -> F/_ y x )
2	1	naecoms 1612	1 |- ( -. A. x x = y -> F/_ y x )

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: (None)