Theorem nfvd 1510

Description: nfv 1509 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 1509	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   F/wnf 1437

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 1426  ax-17 1507

This theorem depends on definitions:  df-bi 116  df-nf 1438

This theorem is referenced by:  sbiedv  1763  cbvaldva  1901  cbvexdva  1902  vtocld  2741  sbcied  2949  nfunid  3751  peano2  4517  iota2d  5121  iota2  5122  riota5f  5762  mpoxopoveq  6145  bdsepnft  13256