Theorem nfvd 1522

Description: nfv 1521 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1578. (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 1521	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1453

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 1442  ax-17 1519

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  sbiedv  1782  cbvaldva  1921  cbvexdva  1922  vtocld  2782  sbcied  2991  nfunid  3803  peano2  4579  iota2d  5185  iota2  5188  riota5f  5833  mpoxopoveq  6219  fproddivapf  11594  bdsepnft  13922