Metamath Proof Explorer


Theorem 3exp2

Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006)

Ref Expression
Hypothesis 3exp2.1 ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion 3exp2 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )

Proof

Step Hyp Ref Expression
1 3exp2.1 ⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜏 )
2 1 ex ⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 ) )
3 2 3expd ⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )