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	⊢ (φ → Ⅎxψ)

Distinct variable group:   ψ,x

Allowed substitution hint:   φ(x)

Proof of Theorem nfvd

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxψ
2	1	a1i 10	1 ⊢ (φ → Ⅎxψ)

Syntax hints:   → wi 4  Ⅎwnf 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  2907  sbcied  3082  nfunid  3898  iota2d  4366  iota2  4367