Theorem 3simpc

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 21-Jun-2022)

	Ref	Expression
Assertion	3simpc	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) )
2	1	3adant1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) )