Theorem nfcvf2 2416

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 2415	. 2 |- ( -. A. y y = x -> F/_ y x )
2	1	naecoms 1776	1 |- ( -. A. x x = y -> F/_ y x )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1400   F/_wnfc 2379

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 623  ax-in2 624  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408  df-nf 1514  df-sb 1816  df-cleq 2231  df-clel 2234  df-nfc 2381

This theorem is referenced by: (None)