Theorem nfcvd 2340

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	⊢ (𝜑 → Ⅎ𝑥𝐴)

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfcvd

Step	Hyp	Ref	Expression
1		nfcv 2339	. 2 ⊢ Ⅎ𝑥𝐴
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝐴)

Syntax hints:   → wi 4  Ⅎwnfc 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-gen 1463  ax-17 1540

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-nfc 2328

This theorem is referenced by:  nfeld  2355  nfraldw  2529  vtoclgft  2814  vtocld  2816  sbcralt  3066  sbcrext  3067  csbied  3131  csbie2t  3133  sbcco3g  3142  csbco3g  3143  dfnfc2  3858  eusvnfb  4490  eusv2i  4491  peano2  4632  iota2d  5246  iota2  5249  fmptcof  5732  riota5f  5905  riota5  5906  fmpoco  6283  nfixpxy  6785  nfnegd  8239  iseqf1olemjpcl  10617  iseqf1olemqpcl  10618  iseqf1olemfvp  10619  seq3f1olemqsum  10622  fprodeq0g  11820  pcmpt  12537  strcollnft  15714