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Theorem nf3andOLD 2221
 Description: Obsolete proof of nf3and 1815 as of 6-Oct-2021. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfandOLD.1 (𝜑 → Ⅎ𝑥𝜓)
nfandOLD.2 (𝜑 → Ⅎ𝑥𝜒)
nfand.3OLD (𝜑 → Ⅎ𝑥𝜃)
Assertion
Ref Expression
nf3andOLD (𝜑 → Ⅎ𝑥(𝜓𝜒𝜃))

Proof of Theorem nf3andOLD
StepHypRef Expression
1 df-3an 1033 . 2 ((𝜓𝜒𝜃) ↔ ((𝜓𝜒) ∧ 𝜃))
2 nfandOLD.1 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
3 nfandOLD.2 . . . 4 (𝜑 → Ⅎ𝑥𝜒)
42, 3nfandOLD 2220 . . 3 (𝜑 → Ⅎ𝑥(𝜓𝜒))
5 nfand.3OLD . . 3 (𝜑 → Ⅎ𝑥𝜃)
64, 5nfandOLD 2220 . 2 (𝜑 → Ⅎ𝑥((𝜓𝜒) ∧ 𝜃))
71, 6nfxfrdOLD 1826 1 (𝜑 → Ⅎ𝑥(𝜓𝜒𝜃))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031  ℲwnfOLD 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-or 384  df-an 385  df-3an 1033  df-ex 1696  df-nf 1701  df-nfOLD 1712 This theorem is referenced by: (None)
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