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Theorem barocoALT 2765
 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
baroco.maj 𝑥(𝜑𝜓)
baroco.min 𝑥(𝜒 ∧ ¬ 𝜓)
Assertion
Ref Expression
barocoALT 𝑥(𝜒 ∧ ¬ 𝜑)

Proof of Theorem barocoALT
StepHypRef Expression
1 baroco.min . 2 𝑥(𝜒 ∧ ¬ 𝜓)
2 baroco.maj . . . . 5 𝑥(𝜑𝜓)
32spi 2185 . . . 4 (𝜑𝜓)
43con3i 157 . . 3 𝜓 → ¬ 𝜑)
54anim2i 619 . 2 ((𝜒 ∧ ¬ 𝜓) → (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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