Theorem nfvd 1578

Description: nfv 1577 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1634. (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 1577	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1509

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 1498  ax-17 1575

This theorem depends on definitions:  df-bi 117  df-nf 1510

This theorem is referenced by:  sbiedv  1837  cbvaldva  1977  cbvexdva  1978  vtocld  2857  sbcied  3069  nfunid  3905  peano2  4699  iota2d  5320  iota2  5323  riota5f  6008  mpoxopoveq  6449  fproddivapf  12255  bdsepnft  16586