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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
StepHypRef Expression
1 nfv 1995 . 2 𝑥𝜓
21a1i 11 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnf 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  4582  iota2d  6018  iota2  6019  riota5f  6782  opiota  7382  mpt2xopoveq  7501  axrepndlem1  9620  axunndlem1  9623  fproddivf  14924  xrofsup  29873  bj-cbvaldvav  33077  bj-cbvexdvav  33078  wl-mo2t  33691  wl-sb8eut  33693  riotasv2d  34765  cdleme42b  36288  dihvalcqpre  37045  mapdheq  37538  hdmap1eq  37611  hdmapval2lem  37641
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