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Theorem nfim1 1479
Description: A closed form of nfim 1480. (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 1428 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfim1.2 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
43nfrd 1429 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
52, 4hbim1 1478 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfi 1367 1 𝑥(𝜑𝜓)
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-5 1352  ax-gen 1354  ax-4 1416  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by:  nfim  1480  cbv1  1648  hbsbd  1874
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