Theorem alimd 1454

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 1452	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		alimd.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	alimdh 1396	1 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1282  Ⅎwnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1376  ax-gen 1378  ax-4 1440

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  alrimdd  1540  moim  2005  ralimdaa  2428  setindft  10760