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Theorem dariiALT 2655
Description: Alternate proof of darii 2654, shorter but using more axioms. This shows how the use of spi 2169 may shorten some proofs of the Aristotelian syllogisms, even though this adds axiom dependencies. Note that spi 2169 is the inference associated with sp 2168, which corresponds to the axiom (T) of modal logic. (Contributed by David A. Wheeler, 27-Aug-2016.) Added precisions on axiom usage. (Revised by BJ, 27-Sep-2022.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
darii.maj 𝑥(𝜑𝜓)
darii.min 𝑥(𝜒𝜑)
Assertion
Ref Expression
dariiALT 𝑥(𝜒𝜓)

Proof of Theorem dariiALT
StepHypRef Expression
1 darii.min . 2 𝑥(𝜒𝜑)
2 darii.maj . . . 4 𝑥(𝜑𝜓)
32spi 2169 . . 3 (𝜑𝜓)
43anim2i 616 . 2 ((𝜒𝜑) → (𝜒𝜓))
51, 4eximii 1831 1 𝑥(𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wal 1531  wex 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774
This theorem is referenced by: (None)
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