Theorem: If a is a real number, then $a\cdot 0=0$.

1. $a\cdot 0+0=a\cdot 0$ (additive identity postulate)

2. $a\cdot 0=a\cdot (0+0)$ (substitution principle)

3. $a\cdot (0+0)=a\cdot 0+a\cdot 0$ (distributive postulate)

4. $a\cdot 0+0=a\cdot 0+a\cdot 0$ I'm lost here, wanna say its the transitive

5. $0+a\cdot 0=a\cdot 0+a\cdot 0$ (commutative postulate of addition)

6. $0=a\cdot 0$ (cancellation property of addition)

7. $a\cdot 0=0$ (symmetric postulate)

So I'm not sure what to put down for the 4th step. The theorem and proof were given and I had to list the postulates for each step.

1. $a\cdot 0+0=a\cdot 0$ (additive identity postulate)

2. $a\cdot 0=a\cdot (0+0)$ (substitution principle)

3. $a\cdot (0+0)=a\cdot 0+a\cdot 0$ (distributive postulate)

4. $a\cdot 0+0=a\cdot 0+a\cdot 0$ I'm lost here, wanna say its the transitive

5. $0+a\cdot 0=a\cdot 0+a\cdot 0$ (commutative postulate of addition)

6. $0=a\cdot 0$ (cancellation property of addition)

7. $a\cdot 0=0$ (symmetric postulate)

So I'm not sure what to put down for the 4th step. The theorem and proof were given and I had to list the postulates for each step.