Theorem exlimdhOLD 2224

Description: Obsolete proof of exlimdh 2149 as of 6-Oct-2021. (Contributed by NM, 28-Jan-1997.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
exlimdhOLD.1	⊢ (𝜑 → ∀𝑥𝜑)
exlimdhOLD.2	⊢ (𝜒 → ∀𝑥𝜒)
exlimdhOLD.3	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

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

Proof of Theorem exlimdhOLD

Step	Hyp	Ref	Expression
1		exlimdhOLD.1	. . 3 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	nfiOLD 1734	. 2 ⊢ Ⅎ𝑥𝜑
3		exlimdhOLD.2	. . 3 ⊢ (𝜒 → ∀𝑥𝜒)
4	3	nfiOLD 1734	. 2 ⊢ Ⅎ𝑥𝜒
5		exlimdhOLD.3	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
6	2, 4, 5	exlimdOLD 2223	1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒))

Syntax hints:   → wi 4  ∀wal 1481  ∃wex 1704

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: (None)