Metamath Proof Explorer


Theorem simp11l

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

Ref Expression
Assertion simp11l ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜏 ∧ 𝜂 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simp1l ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ∧ 𝜃 ) → 𝜑 )
2 1 3ad2ant1 ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜏 ∧ 𝜂 ) → 𝜑 )