Theorem simplrd

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

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

Proof

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