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Theorem nfim1 1463
 Description: A closed form of nfim 1464. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
nfim1.1 𝑥𝜑
nfim1.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfim1 𝑥(𝜑𝜓)

Proof of Theorem nfim1
StepHypRef Expression
1 nfim1.1 . . . 4 𝑥𝜑
21nfri 1412 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfim1.2 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
43nfrd 1413 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
52, 4hbim1 1462 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfi 1351 1 𝑥(𝜑𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4  Ⅎwnf 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-5 1336  ax-gen 1338  ax-4 1400  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350 This theorem is referenced by:  nfim  1464  cbv1  1632  hbsbd  1858
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