Theorem barocoALT 2681

Description: Alternate proof of festino 2678, shorter but using more axioms. See comment of dariiALT 2670. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
baroco.maj	⊢ ∀𝑥(𝜑 → 𝜓)
baroco.min	⊢ ∃𝑥(𝜒 ∧ ¬ 𝜓)

Assertion

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

Proof of Theorem barocoALT

Step	Hyp	Ref	Expression
1		baroco.min	. 2 ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜓)
2		baroco.maj	. . . . 5 ⊢ ∀𝑥(𝜑 → 𝜓)
3	2	spi 2196	. . . 4 ⊢ (𝜑 → 𝜓)
4	3	con3i 154	. . 3 ⊢ (¬ 𝜓 → ¬ 𝜑)
5	4	anim2i 623	. 2 ⊢ ((𝜒 ∧ ¬ 𝜓) → (𝜒 ∧ ¬ 𝜑))
6	1, 5	eximii 1844	1 ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 396  ∀wal 1545  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787

This theorem is referenced by: (None)