Metamath Proof Explorer


Theorem simp33l

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

Ref Expression
Assertion simp33l ( ( 𝜏𝜂 ∧ ( 𝜒𝜃 ∧ ( 𝜑𝜓 ) ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simp3l ( ( 𝜒𝜃 ∧ ( 𝜑𝜓 ) ) → 𝜑 )
2 1 3ad2ant3 ( ( 𝜏𝜂 ∧ ( 𝜒𝜃 ∧ ( 𝜑𝜓 ) ) ) → 𝜑 )