Consider any model
Using semantics of satisfaction this means, for any valuation
Again by semantics of satisfaction, this means that models a truth table for the logical expression shown (of course, rigorously you have to decompose the semantics of all the logical connectives one by one). If the model interpretation is , then:
iff ( or ( and not ))
When the truth table of for the above expression evaluates to true, you can show that
and (not ) implies also evaluates to true.
since the valuation for x was arbitrary