Metamath Proof Explorer

Theorem simp1

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 22-Jun-2022)

Ref Expression
Assertion simp1 ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 id ⊢ ( 𝜑 → 𝜑 )
2 1 3ad2ant1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜑 )