Metamath Proof Explorer


Theorem exp5o

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

Ref Expression
Hypothesis exp5o.1 ( ( 𝜑𝜓𝜒 ) → ( ( 𝜃𝜏 ) → 𝜂 ) )
Assertion exp5o ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) ) ) )

Proof

Step Hyp Ref Expression
1 exp5o.1 ( ( 𝜑𝜓𝜒 ) → ( ( 𝜃𝜏 ) → 𝜂 ) )
2 1 expd ( ( 𝜑𝜓𝜒 ) → ( 𝜃 → ( 𝜏𝜂 ) ) )
3 2 3exp ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) ) ) )