Metamath Proof Explorer


Theorem exp31

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

Ref Expression
Hypothesis exp31.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion exp31 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 exp31.1 ( ( ( 𝜑𝜓 ) ∧ 𝜒 ) → 𝜃 )
2 1 ex ( ( 𝜑𝜓 ) → ( 𝜒𝜃 ) )
3 2 ex ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )