How to derive $¬X \lor ¬Y \lor ¬Y$ from $Z ⊃ (¬X \lor ¬Y)$ and $¬Z ⊃ ¬ Y$ I know that one can derive $¬X \lor ¬Y  \lor ¬Y$ (which simplifies to $¬X \lor ¬Y$, right?) from $Z ⊃ (¬X \lor ¬Y)$ and  $¬Z ⊃ ¬ Y$ but I don't know how you do this. 
Maybe one just has to use constructive dilemma? 

If you have Hypothetical Syllogism and Contraposition, you can do it without having to assume $Z \lor \neg Z$:
$1. Z \rightarrow (\neg X \lor \neg Y) \quad Premise$
$2. \neg Z \rightarrow \neg Y \quad Premise$
$3. Y \rightarrow Z \quad Contraposition \ 2$
$4. Y \rightarrow (\neg X \lor \neg Y) \quad Hypothetical \ Syllogism \ 1,3$
$5. \neg Y \lor \neg X \lor \neg Y \quad Implication \ 4$
$6. \neg X \lor  \neg Y \lor \neg Y \quad Commutation \ 5$
