Theorem alimdh 1563

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 4-Jan-2002.)

Hypotheses

Ref	Expression
alimdh.1	⊢ (φ → ∀xφ)
alimdh.2	⊢ (φ → (ψ → χ))

Assertion

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

Proof of Theorem alimdh

Step	Hyp	Ref	Expression
1		alimdh.1	. 2 ⊢ (φ → ∀xφ)
2		alimdh.2	. . 3 ⊢ (φ → (ψ → χ))
3	2	al2imi 1561	. 2 ⊢ (∀xφ → (∀xψ → ∀xχ))
4	1, 3	syl 15	1 ⊢ (φ → (∀xψ → ∀xχ))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1546  ax-5 1557

This theorem is referenced by:  alrimdh  1587  alimdv  1621  hbald  1740  alimd  1764  dral1  1965  dral1-o  2154  ax11indalem  2197  ax11inda2ALT  2198