Theorem nfvd 1509

Description: nfv 1508 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1564. (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 1436

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 1425  ax-17 1506

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  sbiedv  1762  cbvaldva  1898  cbvexdva  1899  vtocld  2733  sbcied  2940  nfunid  3738  peano2  4504  iota2d  5108  iota2  5109  riota5f  5747  mpoxopoveq  6130  bdsepnft  13074  strcollnft  13171