Theorem nfvd 1996

Description: nfv 1995 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1973. (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nfvd	⊢ (𝜑 → Ⅎ𝑥𝜓)

Distinct variable group:   𝜓,𝑥

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfvd

Step	Hyp	Ref	Expression
1		nfv 1995	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 11	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1856

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-5 1991

This theorem depends on definitions:  df-bi 197  df-ex 1853  df-nf 1858

This theorem is referenced by:  cbvald  2436  sbiedv  2557  vtocld  3408  sbcied  3624  nfunid  4581  iota2d  6019  iota2  6020  riota5f  6779  opiota  7378  mpt2xopoveq  7497  axrepndlem1  9616  axunndlem1  9619  fproddivf  14924  xrofsup  29873  bj-cbvaldvav  33077  bj-cbvexdvav  33078  wl-mo2t  33691  wl-sb8eut  33693  riotasv2d  34765  cdleme42b  36287  dihvalcqpre  37045  mapdheq  37538  hdmap1eq  37611  hdmapval2lem  37641