Metamath Proof Explorer


Theorem simpl11

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 24-Jun-2022)

Ref Expression
Assertion simpl11 ( ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃𝜏 ) ∧ 𝜂 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpl1 ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜂 ) → 𝜑 )
2 1 3ad2antl1 ( ( ( ( 𝜑𝜓𝜒 ) ∧ 𝜃𝜏 ) ∧ 𝜂 ) → 𝜑 )