Theorem alrimddOLD 2195

Description: Obsolete proof of alrimdd 2083 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

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

Proof of Theorem alrimddOLD

Step	Hyp	Ref	Expression
1		alrimddOLD.2	. . 3 ⊢ (𝜑 → Ⅎ𝑥𝜓)
2	1	nfrdOLD 2190	. 2 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))
3		alrimddOLD.1	. . 3 ⊢ Ⅎ𝑥𝜑
4		alrimddOLD.3	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
5	3, 4	alimdOLD 2191	. 2 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))
6	2, 5	syld 47	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1481  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-12 2047

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

This theorem is referenced by:  alrimdOLD  2196