Theorem nfvd 1543

Description: nfv 1542 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1599. (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 1542	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1474

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 1463  ax-17 1540

This theorem depends on definitions:  df-bi 117  df-nf 1475

This theorem is referenced by:  sbiedv  1803  cbvaldva  1943  cbvexdva  1944  vtocld  2816  sbcied  3026  nfunid  3846  peano2  4631  iota2d  5245  iota2  5248  riota5f  5902  mpoxopoveq  6298  fproddivapf  11796  bdsepnft  15533