Theorem nfvd 1509

Description: nfv 1508 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1565. (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 1508	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   F/wnf 1440

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 1429  ax-17 1506

This theorem depends on definitions:  df-bi 116  df-nf 1441

This theorem is referenced by:  sbiedv  1769  cbvaldva  1908  cbvexdva  1909  vtocld  2764  sbcied  2973  nfunid  3779  peano2  4552  iota2d  5157  iota2  5158  riota5f  5798  mpoxopoveq  6181  fproddivapf  11510  bdsepnft  13422