Theorem nfvd 1553

Description: nfv 1552 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1609. (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 1552	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   F/wnf 1484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1473  ax-17 1550

This theorem depends on definitions:  df-bi 117  df-nf 1485

This theorem is referenced by:  sbiedv  1813  cbvaldva  1953  cbvexdva  1954  vtocld  2830  sbcied  3042  nfunid  3871  peano2  4661  iota2d  5277  iota2  5280  riota5f  5947  mpoxopoveq  6349  fproddivapf  12057  bdsepnft  16022