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Theorem nfvd 1467
Description: nfv 1466 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1522. (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 1466 . 2 𝑥𝜓
21a1i 9 1 (𝜑 → Ⅎ𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1394
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 1383  ax-17 1464
This theorem depends on definitions:  df-bi 115  df-nf 1395
This theorem is referenced by:  sbiedv  1719  cbvaldva  1851  cbvexdva  1852  vtocld  2671  sbcied  2873  nfunid  3655  peano2  4400  iota2d  4992  iota2  4993  riota5f  5614  mpt2xopoveq  5987  bdsepnft  11435  strcollnft  11536
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