Theorem alrimd 1589

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

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

Assertion

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

Proof of Theorem alrimd

Step	Hyp	Ref	Expression
1		alrimd.1	. 2 ⊢ Ⅎ𝑥𝜑
2		alrimd.2	. . 3 ⊢ Ⅎ𝑥𝜓
3	2	a1i 9	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
4		alrimd.3	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
5	1, 3, 4	alrimdd 1588	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1329  Ⅎwnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1423  ax-gen 1425  ax-4 1487

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  euexex  2084  ralrimd  2510  fiintim  6817