Theorem nfvd 1422

Description: nfv 1421 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1477. (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 1421	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1349

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-17 1419

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  sbiedv  1672  cbvaldva  1803  cbvexdva  1804  vtocld  2606  sbcied  2799  nfunid  3587  peano2  4318  iota2d  4892  iota2  4893  riota5f  5492  mpt2xopoveq  5855  bdsepnft  10007  strcollnft  10109