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Theorem nfvd 1438
Description: nfv 1437 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1493. (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 1437 . 2 𝑥𝜓
21a1i 9 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-gen 1354  ax-17 1435
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  sbiedv  1688  cbvaldva  1819  cbvexdva  1820  vtocld  2623  sbcied  2821  nfunid  3614  peano2  4345  iota2d  4919  iota2  4920  riota5f  5519  mpt2xopoveq  5885  bdsepnft  10373  strcollnft  10475
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