Theorem nfcvd 2313

Description: If x is disjoint from A, then x is not free in A. (Contributed by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfcvd	|- ( ph -> F/_ x A )

Distinct variable group:   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem nfcvd

Step	Hyp	Ref	Expression
1		nfcv 2312	. 2 |- F/_ x A
2	1	a1i 9	1 |- ( ph -> F/_ x A )

Syntax hints:   -> wi 4   F/_wnfc 2299

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1442  ax-17 1519

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-nfc 2301

This theorem is referenced by:  nfeld  2328  nfraldw  2502  vtoclgft  2780  vtocld  2782  sbcralt  3031  sbcrext  3032  csbied  3095  csbie2t  3097  sbcco3g  3106  csbco3g  3107  dfnfc2  3812  eusvnfb  4437  eusv2i  4438  peano2  4577  iota2d  5183  iota2  5186  fmptcof  5661  riota5f  5831  riota5  5832  fmpoco  6193  nfixpxy  6693  nfnegd  8108  iseqf1olemjpcl  10444  iseqf1olemqpcl  10445  iseqf1olemfvp  10446  seq3f1olemqsum  10449  fprodeq0g  11594  pcmpt  12288  strcollnft  13984