Description: Distribution of negative over subtraction. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negsubdi3d.1 | |- ( ph -> A e. CC ) |
|
negsubdi3d.2 | |- ( ph -> B e. CC ) |
||
Assertion | negsubdi3d | |- ( ph -> -u ( A - B ) = ( -u A - -u B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negsubdi3d.1 | |- ( ph -> A e. CC ) |
|
2 | negsubdi3d.2 | |- ( ph -> B e. CC ) |
|
3 | 1 2 | negsubdi2d | |- ( ph -> -u ( A - B ) = ( B - A ) ) |
4 | 1 2 | neg2subd | |- ( ph -> ( -u A - -u B ) = ( B - A ) ) |
5 | 3 4 | eqtr4d | |- ( ph -> -u ( A - B ) = ( -u A - -u B ) ) |