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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
StepHypRef Expression
1 nfv 1421 . 2 𝑥𝜓
21a1i 9 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 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  9981  strcollnft  10083
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