Metamath Proof Explorer


Theorem simp2ll

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012)

Ref Expression
Assertion simp2ll ( ( 𝜃 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜏 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpll ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜑 )
2 1 3ad2ant2 ⊢ ( ( 𝜃 ∧ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜏 ) → 𝜑 )