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Theorem nfbidOLD 2387
Description: Obsolete proof of nfbid 1981 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 29-Dec-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfbidOLD.1 (𝜑 → Ⅎ𝑥𝜓)
nfbidOLD.2 (𝜑 → Ⅎ𝑥𝜒)
Assertion
Ref Expression
nfbidOLD (𝜑 → Ⅎ𝑥(𝜓𝜒))

Proof of Theorem nfbidOLD
StepHypRef Expression
1 dfbi2 663 . 2 ((𝜓𝜒) ↔ ((𝜓𝜒) ∧ (𝜒𝜓)))
2 nfbidOLD.1 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
3 nfbidOLD.2 . . . 4 (𝜑 → Ⅎ𝑥𝜒)
42, 3nfimdOLD 2371 . . 3 (𝜑 → Ⅎ𝑥(𝜓𝜒))
53, 2nfimdOLD 2371 . . 3 (𝜑 → Ⅎ𝑥(𝜒𝜓))
64, 5nfandOLD 2377 . 2 (𝜑 → Ⅎ𝑥((𝜓𝜒) ∧ (𝜒𝜓)))
71, 6nfxfrdOLD 1987 1 (𝜑 → Ⅎ𝑥(𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383  wnfOLD 1858
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-nfOLD 1870
This theorem is referenced by:  nfbiOLD  2388
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