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Theorem festinoALT 2763
 Description: Alternate proof of festino 2762, shorter but using more axioms. See comment of dariiALT 2754. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
festino.maj 𝑥(𝜑 → ¬ 𝜓)
festino.min 𝑥(𝜒𝜓)
Assertion
Ref Expression
festinoALT 𝑥(𝜒 ∧ ¬ 𝜑)

Proof of Theorem festinoALT
StepHypRef Expression
1 festino.min . 2 𝑥(𝜒𝜓)
2 festino.maj . . . . 5 𝑥(𝜑 → ¬ 𝜓)
32spi 2185 . . . 4 (𝜑 → ¬ 𝜓)
43con2i 141 . . 3 (𝜓 → ¬ 𝜑)
54anim2i 619 . 2 ((𝜒𝜓) → (𝜒 ∧ ¬ 𝜑))
61, 5eximii 1838 1 𝑥(𝜒 ∧ ¬ 𝜑)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 399  ∀wal 1536  ∃wex 1781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782 This theorem is referenced by: (None)
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