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Theorem nfandOLD 2268
Description: Obsolete proof of nfand 1866 as of 6-Oct-2021. (Contributed by Mario Carneiro, 7-Oct-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
nfandOLD.1 (𝜑 → Ⅎ𝑥𝜓)
nfandOLD.2 (𝜑 → Ⅎ𝑥𝜒)
Assertion
Ref Expression
nfandOLD (𝜑 → Ⅎ𝑥(𝜓𝜒))

Proof of Theorem nfandOLD
StepHypRef Expression
1 df-an 385 . 2 ((𝜓𝜒) ↔ ¬ (𝜓 → ¬ 𝜒))
2 nfandOLD.1 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
3 nfandOLD.2 . . . . 5 (𝜑 → Ⅎ𝑥𝜒)
43nfndOLD 2247 . . . 4 (𝜑 → Ⅎ𝑥 ¬ 𝜒)
52, 4nfimdOLD 2262 . . 3 (𝜑 → Ⅎ𝑥(𝜓 → ¬ 𝜒))
65nfndOLD 2247 . 2 (𝜑 → Ⅎ𝑥 ¬ (𝜓 → ¬ 𝜒))
71, 6nfxfrdOLD 1878 1 (𝜑 → Ⅎ𝑥(𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 383  wnfOLD 1749
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750  df-nfOLD 1761
This theorem is referenced by:  nf3andOLD  2269  nfbidOLD  2278
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