Theorem nfcvd 2373

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 2372	. 2 |- F/_ x A
2	1	a1i 9	1 |- ( ph -> F/_ x A )

Syntax hints:   -> wi 4   F/_wnfc 2359

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-gen 1495  ax-17 1572

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-nfc 2361

This theorem is referenced by:  nfeld  2388  nfraldw  2562  vtoclgft  2851  vtocld  2853  sbcralt  3105  sbcrext  3106  csbied  3171  csbie2t  3173  sbcco3g  3182  csbco3g  3183  dfnfc2  3905  eusvnfb  4544  eusv2i  4545  peano2  4686  iota2d  5304  iota2  5307  fmptcof  5801  riotaeqimp  5978  riota5f  5980  riota5  5981  fmpoco  6360  nfixpxy  6862  nfnegd  8338  iseqf1olemjpcl  10725  iseqf1olemqpcl  10726  iseqf1olemfvp  10727  seq3f1olemqsum  10730  fprodeq0g  12144  pcmpt  12861  strcollnft  16305