Theorem simp3d

Description: Deduce a conjunct from a triple conjunction. (Contributed by NM, 4-Sep-2005)

	Ref	Expression
Hypothesis	3simp1d.1	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
Assertion	simp3d	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3simp1d.1	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
2		simp3	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜃 )
3	1 2	syl	⊢ ( 𝜑 → 𝜃 )