Metamath Proof Explorer


Theorem exp512

Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009)

Ref Expression
Hypothesis exp512.1 ( ( 𝜑 ∧ ( ( 𝜓𝜒 ) ∧ ( 𝜃𝜏 ) ) ) → 𝜂 )
Assertion exp512 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) ) ) )

Proof

Step Hyp Ref Expression
1 exp512.1 ( ( 𝜑 ∧ ( ( 𝜓𝜒 ) ∧ ( 𝜃𝜏 ) ) ) → 𝜂 )
2 1 ex ( 𝜑 → ( ( ( 𝜓𝜒 ) ∧ ( 𝜃𝜏 ) ) → 𝜂 ) )
3 2 exp5l ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏𝜂 ) ) ) ) )