Theorem simplbi

Description: Deduction eliminating a conjunct. (Contributed by NM, 27-May-1998)

	Ref	Expression
Hypothesis	simplbi.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
Assertion	simplbi	⊢ ( 𝜑 → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		simplbi.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
2	1	biimpi	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) )
3	2	simpld	⊢ ( 𝜑 → 𝜓 )