Theorem simprbda

Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007)

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

Proof

Step	Hyp	Ref	Expression
1		simplbda.1	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜃 ) ) )
2	1	biimpa	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ∧ 𝜃 ) )
3	2	simpld	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )