Theorem alimd 1509

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
alimd.1	⊢ Ⅎ𝑥𝜑
alimd.2	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
alimd	⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Proof of Theorem alimd

Step	Hyp	Ref	Expression
1		alimd.1	. . 3 ⊢ Ⅎ𝑥𝜑
2	1	nfri 1507	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		alimd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	alimdh 1455	1 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1341  Ⅎwnf 1448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-5 1435  ax-gen 1437  ax-4 1498

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by:  alrimdd  1597  moim  2078  ralimdaa  2532  setindft  13847