Theorem simprrl

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

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

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜒 ∧ 𝜃 ) → 𝜒 )
2	1	ad2antll	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) ) → 𝜒 )