Theorem simplld

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

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

Proof

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