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Theorem nfnanOLD 2274
Description: Obsolete proof of nfnan 1870 as of 6-Oct-2021. (Contributed by Scott Fenton, 2-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfanOLDOLD.1 𝑥𝜑
nfanOLDOLD.2 𝑥𝜓
Assertion
Ref Expression
nfnanOLD 𝑥(𝜑𝜓)

Proof of Theorem nfnanOLD
StepHypRef Expression
1 df-nan 1488 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 nfanOLDOLD.1 . . . 4 𝑥𝜑
3 nfanOLDOLD.2 . . . 4 𝑥𝜓
42, 3nfanOLDOLD 2273 . . 3 𝑥(𝜑𝜓)
54nfnOLD 2246 . 2 𝑥 ¬ (𝜑𝜓)
61, 5nfxfrOLD 1877 1 𝑥(𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 383  wnan 1487  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-nan 1488  df-ex 1745  df-nf 1750  df-nfOLD 1761
This theorem is referenced by: (None)
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