Theorem nfcvf 2644

Description: If and are distinct, then is not free in . (Contributed by Mario Carneiro, 8-Oct-2016.)

Assertion

Ref	Expression
nfcvf

Proof of Theorem nfcvf

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfcv 2619	. 2
2		nfcv 2619	. 2
3		id 22	. 2
4	1, 2, 3	dvelimc 2643	1

Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  F/_wnfc 2605

This theorem is referenced by:  nfcvf2  2645  nfrald  2842  ralcom2  3022  nfreud  3030  nfrmod  3031  nfrmo  3033  nfdisj  4434  nfcvb  4682  nfiotad  5559  nfriotad  6265  nfixp  7508  axextnd  8987  axrepndlem2  8989  axrepnd  8990  axunndlem1  8991  axunnd  8992  axpowndlem2  8994  axpowndlem2OLD  8995  axpowndlem4  8998  axregndlem2  9001  axregnd  9002  axregndOLD  9003  axinfndlem1  9004  axinfnd  9005  axacndlem4  9009  axacndlem5  9010  axacnd  9011  axextdist  29232  bj-nfcsym  34460

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607