Metamath Proof Explorer

Theorem simplr3

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 23-Jun-2022)

Ref Expression
Assertion simplr3 ( ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜏 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 simp3 ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜒 )
2 1 ad2antlr ⊢ ( ( ( 𝜃 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜏 ) → 𝜒 )