Description: A Tseitin axiom for logical exclusive disjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018)
Ref | Expression | ||
---|---|---|---|
Assertion | tsxo3 | |- ( th -> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tsbi3 | |- ( th -> ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) ) |
|
2 | df-xor | |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) ) |
|
3 | 2 | bicomi | |- ( -. ( ph <-> ps ) <-> ( ph \/_ ps ) ) |
4 | 3 | orbi2i | |- ( ( ( ph \/ -. ps ) \/ -. ( ph <-> ps ) ) <-> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) ) |
5 | 1 4 | sylib | |- ( th -> ( ( ph \/ -. ps ) \/ ( ph \/_ ps ) ) ) |