Theorem nfvd 1552

Description: nfv 1551 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1608. (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 1551	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   F/wnf 1483

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 1472  ax-17 1549

This theorem depends on definitions:  df-bi 117  df-nf 1484

This theorem is referenced by:  sbiedv  1812  cbvaldva  1952  cbvexdva  1953  vtocld  2825  sbcied  3035  nfunid  3857  peano2  4643  iota2d  5258  iota2  5261  riota5f  5924  mpoxopoveq  6326  fproddivapf  11942  bdsepnft  15823