Metamath Proof Explorer

Theorem simpl3l

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

Ref Expression
Assertion simpl3l ( ( ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ∧ 𝜏 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpll ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) → 𝜑 )
2 1 3ad2antl3 ⊢ ( ( ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ∧ 𝜏 ) → 𝜑 )