Description: If two complex numbers are unequal, their quotient is not one. Contrapositive of diveq1d . (Contributed by David Moews, 28-Feb-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | div1d.1 | |- ( ph -> A e. CC ) |
|
divcld.2 | |- ( ph -> B e. CC ) |
||
divcld.3 | |- ( ph -> B =/= 0 ) |
||
divne1d.4 | |- ( ph -> A =/= B ) |
||
Assertion | divne1d | |- ( ph -> ( A / B ) =/= 1 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | div1d.1 | |- ( ph -> A e. CC ) |
|
2 | divcld.2 | |- ( ph -> B e. CC ) |
|
3 | divcld.3 | |- ( ph -> B =/= 0 ) |
|
4 | divne1d.4 | |- ( ph -> A =/= B ) |
|
5 | 1 2 3 | diveq1ad | |- ( ph -> ( ( A / B ) = 1 <-> A = B ) ) |
6 | 5 | necon3bid | |- ( ph -> ( ( A / B ) =/= 1 <-> A =/= B ) ) |
7 | 4 6 | mpbird | |- ( ph -> ( A / B ) =/= 1 ) |