Theorem nfvd 1575

Description: nfv 1574 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1631. (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 1574	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1506

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 1495  ax-17 1572

This theorem depends on definitions:  df-bi 117  df-nf 1507

This theorem is referenced by:  sbiedv  1835  cbvaldva  1975  cbvexdva  1976  vtocld  2853  sbcied  3065  nfunid  3894  peano2  4686  iota2d  5304  iota2  5307  riota5f  5980  mpoxopoveq  6384  fproddivapf  12137  bdsepnft  16208