Metamath Proof Explorer


Theorem simpr21

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

Ref Expression
Assertion simpr21 ( ( 𝜂 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpr1 ( ( 𝜂 ∧ ( 𝜑𝜓𝜒 ) ) → 𝜑 )
2 1 3ad2antr2 ( ( 𝜂 ∧ ( 𝜃 ∧ ( 𝜑𝜓𝜒 ) ∧ 𝜏 ) ) → 𝜑 )