Metamath Proof Explorer

Theorem 3simpb

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 21-Jun-2022)

Ref Expression
Assertion 3simpb ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜑 ∧ 𝜒 ) )

Proof

Step Hyp Ref Expression
1 id ⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜑 ∧ 𝜒 ) )
2 1 3adant2 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜑 ∧ 𝜒 ) )