Theorem nfcvf2 2363

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 2362	. 2 |- ( -. A. y y = x -> F/_ y x )
2	1	naecoms 1738	1 |- ( -. A. x x = y -> F/_ y x )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1362   F/_wnfc 2326

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1475  df-sb 1777  df-cleq 2189  df-clel 2192  df-nfc 2328

This theorem is referenced by: (None)