Theorem nfvd 1582

Description: nfv 1581 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1638. (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

Step	Hyp	Ref	Expression
1		nfv 1581	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

This proof depends on syntax axioms:   -> wi 4   F/wnf 1513

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502  ax-17 1579

This proof depends on definitions:  df-bi 117  df-nf 1514

This theorem is used by:  sbiedv  1842  cbvaldva  1984  cbvexdva  1985  vtocld  2875  sbcied  3088  nfunid  3942  peano2  4742  iota2d  5364  iota2  5367  riota5f  6065  mpoxopoveq  6511  fproddivapf  12398  bdsepnft  16913