Question 1193775
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Here is one way to do the derivation 
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td><td>Line(s) Used</td><td>Reason</td></tr><tr><td>1</td><td>(~B v E) -> (C -> G)</td><td></td><td></td></tr><tr><td>2</td><td>(C v D) -> (B -> F)</td><td></td><td></td></tr><tr><td>3</td><td>B v C</td><td></td><td></td></tr><tr><td>4</td><td>~B</td><td></td><td></td></tr><tr><td>:.</td><td>F v G</td><td></td><td></td></tr><tr><td>5</td><td>C</td><td>3,4</td><td>Disjunctive Syllogism</td></tr><tr><td>6</td><td>~B v E</td><td>4</td><td>Addition</td></tr><tr><td>7</td><td>C -> G</td><td>1,6</td><td>Modus Ponens</td></tr><tr><td>8</td><td>C v D</td><td>5</td><td>Addition</td></tr><tr><td>9</td><td>B -> F</td><td>2,8</td><td>Modus Ponens</td></tr><tr><td>10</td><td>(C -> G) & (B -> F)</td><td>7,9</td><td>Conjunction</td></tr><tr><td>11</td><td>C v B</td><td>3,4</td><td>Commutation</td></tr><tr><td>12</td><td>G v F</td><td>10,11</td><td>Constructive Dilemma</td></tr><tr><td>13</td><td>F v G</td><td>12</td><td>Commutation</td></tr></table>
I used arrows in place of the horseshoes
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