that right?

To prove: the sum of two odd integers is even. Using the direct proof technique, we assume x and y are both odd. The statement to be proved is a universally quantified implication. x+y=(2m+1)+(2n+1)=2(m+n+1). To use the UG rule, we consider two arbitrary integers x and y. Proof QED Using the EG/definition/UI/MP rules, x+y is even. Using the definition/UI/MP/EI rules, we let x=2m+1 and y=2n+1, where m and n are integers