Theorem nfvd 1577

Description: nfv 1576 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1633. (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 1576	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1508

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 1497  ax-17 1574

This theorem depends on definitions:  df-bi 117  df-nf 1509

This theorem is referenced by:  sbiedv  1837  cbvaldva  1977  cbvexdva  1978  vtocld  2856  sbcied  3068  nfunid  3900  peano2  4693  iota2d  5313  iota2  5316  riota5f  5997  mpoxopoveq  6405  fproddivapf  12191  bdsepnft  16482