We are almost ready to complete this proof, which would happen on Line $11,$ but we need one more wff for that, which isn't already in the body of our proof.

By citing the rule vI on Line $10,$ which wff could we produce to help us complete this derivation?

$1(1)($R & P$)$ A Aim:

$(($Q v P$)$ & $$T$)$

$2(2)$S A

$3(3)($R $->[$Q & $($T $->$ S$)])$ A

$4(4)($R $->($R & P$))$ A

$1,4(5)$R $1,4$ MT

$1,3,4(6)[$Q & $($T $->$ S$)]3,5$ MT

$1,3,4(7)$ Q $6$ &E

$1,3,4(8)($T $->$ S$)6$ &E

$1,2,3,4(9)$T $2,8$ MT

Remember $-$ Formatting will be important here! So$,$ enter your wff according to the following conventions:

Make sure you put no spaces between symbols.

Good Not Good!

Wffs: $($PvQ$)($ P v Q $),($P v Q$)$

Premises: $1,2,31,2,3$

Rules: $1,2$MP; $5$&E $1,2$ MP; $5$ &E

Use $\text{'}-\text{'}$ for the dash, a single minus sign.

Use $\text{'}$&$\text{'}$ for the ampersand.

Use $\text{'}$v$\text{'}$ for the wedge, a lower$-$case V$.$

Use $\text{'}->\text{'}$ for the arrow. Copy and paste the arrow from here, if you need it in your answer.

Use $\text{'}\text{'}$ for the contradiction symbol. Copy and paste the upside$-$down T from here.

Use $\text{'}\text{'}$ for the turnstile. Copy and paste it from here, if you need it in your answer.

Use $\text{'}$&I$\text{'},\text{'}$&E$\text{'},\text{'}$vI$\text{'},\text{'}$DN$\text{'},\text{'}$MP$\text{'},\text{'}$MT$\text{'},\text{'}$CP$\text{'},\text{'}$IP$\text{'},\text{'}$I$\text{'}$ for the rules.