Metamath Proof Explorer


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 ) ) )