Description: Exclusive-or variant of the law of the excluded middle ( exmid ). This statement is ancient, going back to at least Stoic logic. This statement does not necessarily hold in intuitionistic logic. (Contributed by David A. Wheeler, 23-Feb-2019)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | xorexmid | |- ( ph \/_ -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm5.19 | |- -. ( ph <-> -. ph ) |
|
| 2 | df-xor | |- ( ( ph \/_ -. ph ) <-> -. ( ph <-> -. ph ) ) |
|
| 3 | 1 2 | mpbir | |- ( ph \/_ -. ph ) |