Theorem nfvd 1575

Description: nfv 1574 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1631. (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 1574	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   F/wnf 1506

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 1495  ax-17 1572

This theorem depends on definitions:  df-bi 117  df-nf 1507

This theorem is referenced by:  sbiedv  1835  cbvaldva  1975  cbvexdva  1976  vtocld  2853  sbcied  3065  nfunid  3895  peano2  4687  iota2d  5305  iota2  5308  riota5f  5981  mpoxopoveq  6386  fproddivapf  12142  bdsepnft  16250