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Theorem cesaroOLD 2713
 Description: Obsolete proof of cesaro 2712 as of 27-Sep-2022. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
cesaro.maj 𝑥(𝜑 → ¬ 𝜓)
cesaro.min 𝑥(𝜒𝜓)
cesaro.e 𝑥𝜒
Assertion
Ref Expression
cesaroOLD 𝑥(𝜒 ∧ ¬ 𝜑)

Proof of Theorem cesaroOLD
StepHypRef Expression
1 cesaro.e . 2 𝑥𝜒
2 cesaro.maj . . . . 5 𝑥(𝜑 → ¬ 𝜓)
32spi 2168 . . . 4 (𝜑 → ¬ 𝜓)
4 cesaro.min . . . . 5 𝑥(𝜒𝜓)
54spi 2168 . . . 4 (𝜒𝜓)
63, 5nsyl3 136 . . 3 (𝜒 → ¬ 𝜑)
76ancli 544 . 2 (𝜒 → (𝜒 ∧ ¬ 𝜑))
81, 7eximii 1880 1 𝑥(𝜒 ∧ ¬ 𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 386  ∀wal 1599  ∃wex 1823 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-12 2163 This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824 This theorem is referenced by: (None)
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