Metamath Proof Explorer

Theorem simprl1

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 23-Jun-2022)

Ref Expression
Assertion simprl1 ( ( 𝜏 ∧ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simp1 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜑 )
2 1 ad2antrl ⊢ ( ( 𝜏 ∧ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ) → 𝜑 )