Theorem nfvd 1462

Description: nfv 1461 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1517. (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 1461	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1378  ax-17 1459

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  sbiedv  1712  cbvaldva  1844  cbvexdva  1845  vtocld  2651  sbcied  2850  nfunid  3608  peano2  4336  iota2d  4912  iota2  4913  riota5f  5512  mpt2xopoveq  5878  bdsepnft  10678  strcollnft  10779