Prove the following two-qubit identities
CNOTx₁CNOT=x₁x₂
CNOTy₁CNOT=y₁x₂
CNOTz₁CNOT=z₁1₂
CNOTx₂CNOT=1₁x₂
CNOTy₂CNOT=z₁y₂
CNOTz₂CNOT=z₁z₂
where CNOT uses qubit 1 as the control qubit and qubit 2 as the target qubit, the subscript in the operators denotes the qubit (e.g. x₂ is Pauli σₓ for the 2nd qubit).