Metamath Proof Explorer

Theorem simpr31

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

Ref Expression
Assertion simpr31 ( ( 𝜂 ∧ ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpr1 ⊢ ( ( 𝜂 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) → 𝜑 )
2 1 3ad2antr3 ⊢ ( ( 𝜂 ∧ ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ) → 𝜑 )