Theorem cesaroOLD 2713

Description: Obsolete proof of cesaro 2712 as of 27-Sep-2022. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
cesaro.maj	⊢ ∀𝑥(𝜑 → ¬ 𝜓)
cesaro.min	⊢ ∀𝑥(𝜒 → 𝜓)
cesaro.e	⊢ ∃𝑥𝜒

Assertion

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

Proof of Theorem cesaroOLD

Step	Hyp	Ref	Expression
1		cesaro.e	. 2 ⊢ ∃𝑥𝜒
2		cesaro.maj	. . . . 5 ⊢ ∀𝑥(𝜑 → ¬ 𝜓)
3	2	spi 2168	. . . 4 ⊢ (𝜑 → ¬ 𝜓)
4		cesaro.min	. . . . 5 ⊢ ∀𝑥(𝜒 → 𝜓)
5	4	spi 2168	. . . 4 ⊢ (𝜒 → 𝜓)
6	3, 5	nsyl3 136	. . 3 ⊢ (𝜒 → ¬ 𝜑)
7	6	ancli 544	. 2 ⊢ (𝜒 → (𝜒 ∧ ¬ 𝜑))
8	1, 7	eximii 1880	1 ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 386  ∀wal 1599  ∃wex 1823

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-12 2163

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824

This theorem is referenced by: (None)