Metamath Proof Explorer


Theorem exp4a

Description: An exportation inference. (Contributed by NM, 26-Apr-1994) (Proof shortened by Wolf Lammen, 20-Jul-2021)

Ref Expression
Hypothesis exp4a.1 ⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) )
Assertion exp4a ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step Hyp Ref Expression
1 exp4a.1 ⊢ ( 𝜑 → ( 𝜓 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) ) )
2 1 imp ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
3 2 exp4b ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )