Theorem nfvd 1551

Description: nfv 1550 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1607. (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 1550	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1482

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 1471  ax-17 1548

This theorem depends on definitions:  df-bi 117  df-nf 1483

This theorem is referenced by:  sbiedv  1811  cbvaldva  1951  cbvexdva  1952  vtocld  2824  sbcied  3034  nfunid  3856  peano2  4641  iota2d  5255  iota2  5258  riota5f  5914  mpoxopoveq  6316  fproddivapf  11861  bdsepnft  15687