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Theorem nfvd 1419
Description: nfv 1418 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders such as nfimd 1474. (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 1418 . 2 xψ
21a1i 9 1 (φ → Ⅎxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1346
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 1335  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  sbiedv  1669  cbvaldva  1800  cbvexdva  1801  vtocld  2600  sbcied  2793  nfunid  3578  peano2  4261  iota2d  4835  iota2  4836  riota5f  5435  mpt2xopoveq  5796  bdsepnft  9321  strcollnft  9414
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