Metamath Proof Explorer


Theorem simp3r2

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

Ref Expression
Assertion simp3r2 ( ( 𝜏𝜂 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ) ) → 𝜓 )

Proof

Step Hyp Ref Expression
1 simpr2 ( ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ) → 𝜓 )
2 1 3ad2ant3 ( ( 𝜏𝜂 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ) ) → 𝜓 )