Metamath Proof Explorer


Theorem simp233

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

Ref Expression
Assertion simp233 ( ( 𝜂 ∧ ( 𝜃𝜏 ∧ ( 𝜑𝜓𝜒 ) ) ∧ 𝜁 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simp33 ( ( 𝜃𝜏 ∧ ( 𝜑𝜓𝜒 ) ) → 𝜒 )
2 1 3ad2ant2 ( ( 𝜂 ∧ ( 𝜃𝜏 ∧ ( 𝜑𝜓𝜒 ) ) ∧ 𝜁 ) → 𝜒 )