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Theorem nfvd 1674
Description: nfv 1673 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1850. (Contributed by Mario Carneiro, 6-Oct-2016.)
Assertion
Ref Expression
nfvd  |-  ( ph  ->  F/ x ps )
Distinct variable group:    ps, x
Allowed substitution hint:    ph( x)

Proof of Theorem nfvd
StepHypRef Expression
1 nfv 1673 . 2  |-  F/ x ps
21a1i 11 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F/wnf 1589
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-5 1670
This theorem depends on definitions:  df-bi 185  df-nf 1590
This theorem is referenced by:  cbvaldva  1980  cbvexdva  1981  sbiedv  2104  vtocld  3022  sbcied  3223  nfunid  4098  iota2d  5406  iota2  5407  riota5f  6077  opiota  6633  mpt2xopoveq  6736  axrepndlem1  8756  axunndlem1  8759  xrofsup  26055  wl-mo2t  28396  wl-sb8eut  28398  bj-cbvaldvav  32242  bj-cbvexdvav  32243  riotasv2d  32608  cdleme42b  34122  dihvalcqpre  34880  mapdheq  35373  hdmap1eq  35447  hdmapval2lem  35479
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