Theorem alrimdd 1768

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

Hypotheses

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

Assertion

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

Proof of Theorem alrimdd

Step	Hyp	Ref	Expression
1		alrimdd.2	. . 3 ⊢ (φ → Ⅎxψ)
2	1	nfrd 1763	. 2 ⊢ (φ → (ψ → ∀xψ))
3		alrimdd.1	. . 3 ⊢ Ⅎxφ
4		alrimdd.3	. . 3 ⊢ (φ → (ψ → χ))
5	3, 4	alimd 1764	. 2 ⊢ (φ → (∀xψ → ∀xχ))
6	2, 5	syld 40	1 ⊢ (φ → (ψ → ∀xχ))

Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  alrimd  1769  19.23tOLD  1819