Metamath Proof Explorer


Theorem simp12r

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

Ref Expression
Assertion simp12r ( ( ( 𝜒 ∧ ( 𝜑𝜓 ) ∧ 𝜃 ) ∧ 𝜏𝜂 ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 simp2r ( ( 𝜒 ∧ ( 𝜑𝜓 ) ∧ 𝜃 ) → 𝜓 )
2 1 3ad2ant1 ( ( ( 𝜒 ∧ ( 𝜑𝜓 ) ∧ 𝜃 ) ∧ 𝜏𝜂 ) → 𝜓 )