Theorem alrimdOLD 2184

Description: Obsolete proof of alrimd 2071 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
alrimdOLD.1	⊢ Ⅎ𝑥𝜑
alrimdOLD.2	⊢ Ⅎ𝑥𝜓
alrimdOLD.3	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
alrimdOLD	⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimdOLD

Step	Hyp	Ref	Expression
1		alrimdOLD.1	. 2 ⊢ Ⅎ𝑥𝜑
2		alrimdOLD.2	. . 3 ⊢ Ⅎ𝑥𝜓
3	2	a1i 11	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
4		alrimdOLD.3	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
5	1, 3, 4	alrimddOLD 2183	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1473  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712

This theorem is referenced by:  nfimdOLD  2214