(1). (I&E) > ~ F
(2). F v (G&H)
(3). I = E / (conclusion) I > G
(4). | I Assumption for Conditional Proof
(5). | (I>E)&(E>I) (3),Material Equivalence
(6). | I>E (5),Simplification
(7). | E (6),(4),Modus Ponens
(8). | I&E (4),(7),Conjunction
(9). | ~F (1),(8),Modus Ponens
(10). | G&H (2),(9),Disjunctive Syllogism
(11). | G (10),Simplification
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(12). I > G Conditional Proof (4)-(11)
Edwin