-------------------

NOTE: Using

  & for "AND" 

  v for "OR"

  --> for  "implies"

-------------------



1. ~B v ((C-->D) & (E-->D))  Premise

2. B & (C v E)               Premise

3. B                         2 Simplification (SIMP)

4. ((C-->D) & (E-->D))       3,1 Conditional Disjunction (CD)

5. C v E                     2 SIMP

6. :: C                      Conditional Proof (CP) assumption #1

7. :: D                      6,4 Modus Ponens (MP)

8. :: E                      CP assumption #2

9. :: D                      8,4 MP

10.:: (C V E) --> D          6-9 Proof by Cases (PBC)

11. D                        5,6-10  CP



 

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