Metamath Proof Explorer


Theorem simp222

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

Ref Expression
Assertion simp222 ( ( 𝜂 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) ∧ 𝜁 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 simp22 ( ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) → 𝜓 )
2 1 3ad2ant2 ( ( 𝜂 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) ∧ 𝜁 ) → 𝜓 )