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Theorem nfim1OLD 2216
Description: Obsolete proof of nfim1 2055 as of 6-Oct-2021. (Contributed by NM, 2-Jun-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
nfim1OLD.1 𝑥𝜑
nfim1OLD.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfim1OLD 𝑥(𝜑𝜓)

Proof of Theorem nfim1OLD
StepHypRef Expression
1 nfim1OLD.1 . . . 4 𝑥𝜑
21nfriOLD 2177 . . 3 (𝜑 → ∀𝑥𝜑)
3 nfim1OLD.2 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
43nfrdOLD 2178 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
52, 4hbim1OLD 2215 . 2 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
65nfiOLD 1725 1 𝑥(𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnfOLD 1700
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712
This theorem is referenced by:  nfimOLD  2217
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