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Theorem cesareOLD 2729
Description: Obsolete proof of cesare 2728 as of 27-Sep-2022. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
cesare.maj 𝑥(𝜑 → ¬ 𝜓)
cesare.min 𝑥(𝜒𝜓)
Assertion
Ref Expression
cesareOLD 𝑥(𝜒 → ¬ 𝜑)

Proof of Theorem cesareOLD
StepHypRef Expression
1 cesare.maj . . . 4 𝑥(𝜑 → ¬ 𝜓)
21spi 2218 . . 3 (𝜑 → ¬ 𝜓)
3 cesare.min . . . 4 𝑥(𝜒𝜓)
43spi 2218 . . 3 (𝜒𝜓)
52, 4nsyl3 136 . 2 (𝜒 → ¬ 𝜑)
65ax-gen 1891 1 𝑥(𝜒 → ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-12 2213
This theorem depends on definitions:  df-bi 199  df-ex 1876
This theorem is referenced by: (None)
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