Metamath Proof Explorer

Theorem simpr3l

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

Ref Expression
Assertion simpr3l ( ( 𝜏 ∧ ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ) → 𝜑 )

Proof

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