Metamath Proof Explorer


Theorem simpr33

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

Ref Expression
Assertion simpr33 ( ( 𝜂 ∧ ( 𝜃𝜏 ∧ ( 𝜑𝜓𝜒 ) ) ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simpr3 ( ( 𝜂 ∧ ( 𝜑𝜓𝜒 ) ) → 𝜒 )
2 1 3ad2antr3 ( ( 𝜂 ∧ ( 𝜃𝜏 ∧ ( 𝜑𝜓𝜒 ) ) ) → 𝜒 )