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Theorem calemosOLD 2723
 Description: Obsolete proof of calemos 2722 as of 16-Sep-2022. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
calemos.maj 𝑥(𝜑𝜓)
calemos.min 𝑥(𝜓 → ¬ 𝜒)
calemos.e 𝑥𝜒
Assertion
Ref Expression
calemosOLD 𝑥(𝜒 ∧ ¬ 𝜑)

Proof of Theorem calemosOLD
StepHypRef Expression
1 calemos.e . 2 𝑥𝜒
2 calemos.min . . . . . 6 𝑥(𝜓 → ¬ 𝜒)
32spi 2216 . . . . 5 (𝜓 → ¬ 𝜒)
43con2i 136 . . . 4 (𝜒 → ¬ 𝜓)
5 calemos.maj . . . . 5 𝑥(𝜑𝜓)
65spi 2216 . . . 4 (𝜑𝜓)
74, 6nsyl 137 . . 3 (𝜒 → ¬ 𝜑)
87ancli 544 . 2 (𝜒 → (𝜒 ∧ ¬ 𝜑))
91, 8eximii 1931 1 𝑥(𝜒 ∧ ¬ 𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 384  ∀wal 1650  ∃wex 1874 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-12 2211 This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875 This theorem is referenced by: (None)
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