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 | dfnan2 | |- ( ( ph -/\ ps ) <-> ( ph -> -. ps ) ) |
|
3 | dfnan2 | |- ( ( ps -/\ ph ) <-> ( ps -> -. ph ) ) |
|
4 | 1 2 3 | 3bitr4i | |- ( ( ph -/\ ps ) <-> ( ps -/\ ph ) ) |