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Theorem nfvd 1492
Description: nfv 1491 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1547. (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 1491 . 2  |-  F/ x ps
21a1i 9 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1419
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1408  ax-17 1489
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  sbiedv  1745  cbvaldva  1878  cbvexdva  1879  vtocld  2710  sbcied  2915  nfunid  3711  peano2  4477  iota2d  5081  iota2  5082  riota5f  5720  mpoxopoveq  6103  bdsepnft  12887  strcollnft  12984
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