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Theorem nfvd 1509
Description: nfv 1508 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1564. (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
StepHypRef Expression
1 nfv 1508 . 2 𝑥𝜓
21a1i 9 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1425  ax-17 1506
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  sbiedv  1762  cbvaldva  1898  cbvexdva  1899  vtocld  2733  sbcied  2940  nfunid  3738  peano2  4504  iota2d  5108  iota2  5109  riota5f  5747  mpoxopoveq  6130  bdsepnft  13074  strcollnft  13171
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