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Theorem nf3orOLD 2386
 Description: Obsolete proof of nf3or 1980 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfOLD.1 𝑥𝜑
nfOLD.2 𝑥𝜓
nfOLD.3 𝑥𝜒
Assertion
Ref Expression
nf3orOLD 𝑥(𝜑𝜓𝜒)

Proof of Theorem nf3orOLD
StepHypRef Expression
1 df-3or 1073 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
2 nfOLD.1 . . . 4 𝑥𝜑
3 nfOLD.2 . . . 4 𝑥𝜓
42, 3nforOLD 2385 . . 3 𝑥(𝜑𝜓)
5 nfOLD.3 . . 3 𝑥𝜒
64, 5nforOLD 2385 . 2 𝑥((𝜑𝜓) ∨ 𝜒)
71, 6nfxfrOLD 1982 1 𝑥(𝜑𝜓𝜒)
 Colors of variables: wff setvar class Syntax hints:   ∨ wo 382   ∨ w3o 1071  ℲwnfOLD 1854 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-10 2164  ax-12 2192 This theorem depends on definitions:  df-bi 197  df-or 384  df-3or 1073  df-ex 1850  df-nf 1855  df-nfOLD 1866 This theorem is referenced by: (None)
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