Description: Alternative denial is commutative. Remark: alternative denial is not associative, see nanass . (Contributed by Mario Carneiro, 9-May-2015) (Proof shortened by Wolf Lammen, 26-Jun-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nancom | |- ( ( ph -/\ ps ) <-> ( ps -/\ ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | con2b | |- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) ) |
|
| 2 | nanimn | |- ( ( ph -/\ ps ) <-> ( ph -> -. ps ) ) |
|
| 3 | nanimn | |- ( ( ps -/\ ph ) <-> ( ps -> -. ph ) ) |
|
| 4 | 1 2 3 | 3bitr4i | |- ( ( ph -/\ ps ) <-> ( ps -/\ ph ) ) |