Theorem alrimd 1769

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 10	. 2 ⊢ (φ → Ⅎxψ)
4		alrimd.3	. 2 ⊢ (φ → (ψ → χ))
5	1, 3, 4	alrimdd 1768	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:  nfimd  1808  moexex  2273  ralrimd  2703