Theorem simpr2

Description: Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Assertion	simpr2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		simpr	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜒 )
2	1	3ad2antr2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜒 )