1. (A v B) --> C Premise
2. (~A v D) --> E Premise
// show C v E
// I am using a conditional proof, lines prefixed with :: are part
// of the conditional proof.
3.:: A Conditional Proof (CP) assumption #1
4.:: (A v B) 3, ADDition
5.:: C 4,1 Modus Ponens (MP)
6.:: ~A CP assumption #2
7.:: (~A v D) 6, ADD
8.:: E 7,2 MP
9.:: C v E 3-8, Proof by Cases (PBC)
10. C v E 3-9, CP
// Explanation:
// Lines 3-5 show that assuming A true results in C true
// Lines 6-8 show that assuming A false results in E true
// Line 9 says "A or ~A" results in "C or E" true. Note
// that A or ~A must be true.
