Description: Distribution of negative over subtraction. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negidd.1 | |- ( ph -> A e. CC ) |
|
pncand.2 | |- ( ph -> B e. CC ) |
||
Assertion | negsubdid | |- ( ph -> -u ( A - B ) = ( -u A + B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | |- ( ph -> A e. CC ) |
|
2 | pncand.2 | |- ( ph -> B e. CC ) |
|
3 | negsubdi | |- ( ( A e. CC /\ B e. CC ) -> -u ( A - B ) = ( -u A + B ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> -u ( A - B ) = ( -u A + B ) ) |