Conjunction elimination rule

The conjunction elimination rule in natural deduction permits both inferencesThe symbol $\wedge$ denotes logical conjunction. A proof of the conjunction supplies each of its component propositions, so either component can be used in a later argument.

For example, from $0<x\wedge x<1$ one can infer $0<x$ when establishing positivity, and separately infer $x<1$ when establishing an upper bound. The truth table makes the rule sound: every assignment satisfying the conjunction satisfies both components.