Theorem simprll

Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009)

	Ref	Expression
Assertion	simprll	⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜓 )
2	1	ad2antrl	⊢ ( ( 𝜑 ∧ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) → 𝜓 )