Theorem prtlem60

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

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

Proof

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