Theorem nfvd 1582

Description: nfv 1581 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1638. (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 1581	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1513

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 1502  ax-17 1579

This theorem depends on definitions:  df-bi 117  df-nf 1514

This theorem is referenced by:  sbiedv  1842  cbvaldva  1984  cbvexdva  1985  vtocld  2875  sbcied  3088  nfunid  3937  peano2  4737  iota2d  5359  iota2  5362  riota5f  6055  mpoxopoveq  6501  fproddivapf  12376  bdsepnft  16827