Metamath Proof Explorer


Theorem exp43

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

Ref Expression
Hypothesis exp43.1 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion exp43 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step Hyp Ref Expression
1 exp43.1 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
2 1 ex ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )
3 2 exp4b ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )