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