Theorem nfvd 1467

Description: nfv 1466 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1522. (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 1466	. 2 |- F/ x ps
2	1	a1i 9	1 |- ( ph -> F/ x ps )

Syntax hints:   -> wi 4   F/wnf 1394

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1383  ax-17 1464

This theorem depends on definitions:  df-bi 115  df-nf 1395

This theorem is referenced by:  sbiedv  1719  cbvaldva  1851  cbvexdva  1852  vtocld  2671  sbcied  2875  nfunid  3658  peano2  4408  iota2d  5000  iota2  5001  riota5f  5624  mpt2xopoveq  5997  bdsepnft  11661  strcollnft  11762