Theorem nfvd 1620

Description: nfv 1619 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1808. (Contributed by Mario Carneiro, 6-Oct-2016.)

Assertion

Ref	Expression
nfvd	|- (ph -> F/xps)

Distinct variable group:   ps,x

Allowed substitution hint:   ph(x)

Proof of Theorem nfvd

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 |- F/xps
2	1	a1i 10	1 |- (ph -> F/xps)

Syntax hints:   -> wi 4   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-17 1616

This theorem depends on definitions:  df-bi 177  df-nf 1545

This theorem is referenced by:  cbvald  2008  cbvaldva  2010  cbvexdva  2011  sbiedv  2037  vtocld  2908  sbcied  3083  nfunid  3899  iota2d  4367  iota2  4368