Metamath Proof Explorer


Theorem simp111

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

Ref Expression
Assertion simp111 ( ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃𝜏 ) ∧ 𝜂𝜁 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simp11 ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃𝜏 ) → 𝜑 )
2 1 3ad2ant1 ( ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃𝜏 ) ∧ 𝜂𝜁 ) → 𝜑 )