1. ~F --> G

2.  F --> H

3.:: ~F       Conditional Proof (CP) assumption #1

4.:: G        3,1 Modus Ponens (MP)

5.:: F        CP, assumption #2

6.:: H        5,2 MP

7.:: G v H    3-4 and 5-6, Proof by Cases (PBC)

8. G v H      3-7 CP 



In words: if we assume ~F, G must be true.  If we assume F, then H must be true.  Since F v ~F must be true, G v H must be true.



  

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