Theorem nfvd 1553

Description: nfv 1552 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1609. (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 1552	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1484

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 1473  ax-17 1550

This theorem depends on definitions:  df-bi 117  df-nf 1485

This theorem is referenced by:  sbiedv  1813  cbvaldva  1953  cbvexdva  1954  vtocld  2827  sbcied  3039  nfunid  3863  peano2  4651  iota2d  5267  iota2  5270  riota5f  5937  mpoxopoveq  6339  fproddivapf  12017  bdsepnft  15961