Theorem nfvd 1517

Description: nfv 1516 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1573. (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 1516	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1437  ax-17 1514

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by:  sbiedv  1777  cbvaldva  1916  cbvexdva  1917  vtocld  2778  sbcied  2987  nfunid  3796  peano2  4572  iota2d  5178  iota2  5179  riota5f  5822  mpoxopoveq  6208  fproddivapf  11572  bdsepnft  13769