Metamath Proof Explorer

Theorem simpl31

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

Ref Expression
Assertion simpl31 ( ( ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜂 ) → 𝜑 )

Proof

Step Hyp Ref Expression
1 simpl1 ⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜂 ) → 𝜑 )
2 1 3ad2antl3 ⊢ ( ( ( 𝜃 ∧ 𝜏 ∧ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ∧ 𝜂 ) → 𝜑 )