Theorem simprld

Description: Deduction eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypothesis	simprld.1	⊢ ( 𝜑 → ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) )
Assertion	simprld	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		simprld.1	⊢ ( 𝜑 → ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) )
2	1	simprd	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜃 ) )
3	2	simpld	⊢ ( 𝜑 → 𝜒 )