Theorem exlimdOLD 2223

Description: Obsolete proof of exlimd 2087 as of 6-Oct-2021. (Contributed by NM, 23-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 12-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
exlimdOLD.1	⊢ Ⅎ𝑥𝜑
exlimdOLD.2	⊢ Ⅎ𝑥𝜒
exlimdOLD.3	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
exlimdOLD	⊢ (𝜑 → (∃𝑥𝜓 → 𝜒))

Proof of Theorem exlimdOLD

Step	Hyp	Ref	Expression
1		exlimdOLD.1	. . 3 ⊢ Ⅎ𝑥𝜑
2		exlimdOLD.3	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	eximdOLD 2197	. 2 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))
4		exlimdOLD.2	. . 3 ⊢ Ⅎ𝑥𝜒
5	4	19.9OLD 2205	. 2 ⊢ (∃𝑥𝜒 ↔ 𝜒)
6	3, 5	syl6ib 241	1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒))

Syntax hints:   → wi 4  ∃wex 1704  ℲwnfOLD 1709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nfOLD 1721

This theorem is referenced by:  exlimdhOLD  2224