Theorem festinoALT 2665

Description: Alternate proof of festino 2664, shorter but using more axioms. See comment of dariiALT 2656. (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(𝜒 ∧ 𝜓)

Assertion

Ref	Expression
festinoALT	⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑)

Proof of Theorem festinoALT

Step	Hyp	Ref	Expression
1		festino.min	. 2 ⊢ ∃𝑥(𝜒 ∧ 𝜓)
2		festino.maj	. . . . 5 ⊢ ∀𝑥(𝜑 → ¬ 𝜓)
3	2	spi 2170	. . . 4 ⊢ (𝜑 → ¬ 𝜓)
4	3	con2i 139	. . 3 ⊢ (𝜓 → ¬ 𝜑)
5	4	anim2i 616	. 2 ⊢ ((𝜒 ∧ 𝜓) → (𝜒 ∧ ¬ 𝜑))
6	1, 5	eximii 1832	1 ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 395  ∀wal 1532  ∃wex 1774

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-12 2164

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1775

This theorem is referenced by: (None)