Theorem prtlem60 33152

Description: Lemma for prter3 33185. (Contributed by Rodolfo Medina, 9-Oct-2010.)

Hypotheses

Ref	Expression
prtlem60.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
prtlem60.2	⊢ (𝜓 → (𝜃 → 𝜏))

Assertion

Ref	Expression
prtlem60	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))

Proof of Theorem prtlem60

Step	Hyp	Ref	Expression
1		prtlem60.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		prtlem60.2	. . 3 ⊢ (𝜓 → (𝜃 → 𝜏))
3	2	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏)))
4	1, 3	syldd 70	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))

Syntax hints:   → wi 4

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

This theorem is referenced by: (None)