Theorem nfvd 1529

Description: nfv 1528 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1585. (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 1528	. 2 ⊢ Ⅎ𝑥𝜓
2	1	a1i 9	1 ⊢ (𝜑 → Ⅎ𝑥𝜓)

Syntax hints:   → wi 4  Ⅎwnf 1460

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 1449  ax-17 1526

This theorem depends on definitions:  df-bi 117  df-nf 1461

This theorem is referenced by:  sbiedv  1789  cbvaldva  1928  cbvexdva  1929  vtocld  2790  sbcied  3000  nfunid  3817  peano2  4595  iota2d  5204  iota2  5207  riota5f  5855  mpoxopoveq  6241  fproddivapf  11639  bdsepnft  14642