Metamath Proof Explorer


Theorem simp3l1

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

Ref Expression
Assertion simp3l1 ( ( 𝜏𝜂 ∧ ( ( 𝜑𝜓𝜒 ) ∧ 𝜃 ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpl1 ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃 ) → 𝜑 )
2 1 3ad2ant3 ( ( 𝜏𝜂 ∧ ( ( 𝜑𝜓𝜒 ) ∧ 𝜃 ) ) → 𝜑 )