Theorem simprbi

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

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

Proof

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