Description: Distribution of negative over subtraction. (Contributed by NM, 6-Aug-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negidi.1 | |- A e. CC |
|
pncan3i.2 | |- B e. CC |
||
Assertion | negsubdii | |- -u ( A - B ) = ( -u A + B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidi.1 | |- A e. CC |
|
2 | pncan3i.2 | |- B e. CC |
|
3 | 2 | negcli | |- -u B e. CC |
4 | 1 3 | negdii | |- -u ( A + -u B ) = ( -u A + -u -u B ) |
5 | 1 2 | negsubi | |- ( A + -u B ) = ( A - B ) |
6 | 5 | negeqi | |- -u ( A + -u B ) = -u ( A - B ) |
7 | 2 | negnegi | |- -u -u B = B |
8 | 7 | oveq2i | |- ( -u A + -u -u B ) = ( -u A + B ) |
9 | 4 6 8 | 3eqtr3i | |- -u ( A - B ) = ( -u A + B ) |