Metamath Proof Explorer


Theorem simp1l3

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

Ref Expression
Assertion simp1l3 ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ∧ 𝜂 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simpl3 ⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜒 )
2 1 3ad2ant1 ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ∧ 𝜂 ) → 𝜒 )