Theorem simp1bi

Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

	Ref	Expression
Hypothesis	3simp1bi.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
Assertion	simp1bi	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		3simp1bi.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) )
3	2	simp1d	⊢ ( 𝜑 → 𝜓 )