Description: Move negative sign inside of a division. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | div1d.1 | |- ( ph -> A e. CC ) |
|
divcld.2 | |- ( ph -> B e. CC ) |
||
divcld.3 | |- ( ph -> B =/= 0 ) |
||
Assertion | divnegd | |- ( ph -> -u ( A / B ) = ( -u A / B ) ) |
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 | divneg | |- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> -u ( A / B ) = ( -u A / B ) ) |
|
5 | 1 2 3 4 | syl3anc | |- ( ph -> -u ( A / B ) = ( -u A / B ) ) |