Metamath Proof Explorer


Theorem simp321

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

Ref Expression
Assertion simp321 ( ( 𝜂𝜁 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simp21 ( ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) → 𝜑 )
2 1 3ad2ant3 ( ( 𝜂𝜁 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) ) → 𝜑 )