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