Theorem al2im 1814

Description: Closed form of al2imi 1815. Version of alim 1810 for a nested implication. (Contributed by Alan Sare, 31-Dec-2011.)

Assertion

Ref	Expression
al2im	⊢ (∀𝑥(𝜑 → (𝜓 → 𝜒)) → (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)))

Proof of Theorem al2im

Step	Hyp	Ref	Expression
1		alim 1810	. 2 ⊢ (∀𝑥(𝜑 → (𝜓 → 𝜒)) → (∀𝑥𝜑 → ∀𝑥(𝜓 → 𝜒)))
2		alim 1810	. 2 ⊢ (∀𝑥(𝜓 → 𝜒) → (∀𝑥𝜓 → ∀𝑥𝜒))
3	1, 2	syl6 35	1 ⊢ (∀𝑥(𝜑 → (𝜓 → 𝜒)) → (∀𝑥𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)))

Syntax hints:   → wi 4  ∀wal 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1809

This theorem is referenced by:  al2imi  1815  bj-alanim  36635  al3im  43638  19.41rgVD  44893