Description: Relationship between subtraction and negative. Theorem I.3 of Apostol p. 18. (Contributed by NM, 26-Nov-1994) (Proof shortened by Andrew Salmon, 22-Oct-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | negidi.1 | |- A e. CC |
|
| pncan3i.2 | |- B e. CC |
||
| Assertion | negsubi | |- ( A + -u B ) = ( A - B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | negidi.1 | |- A e. CC |
|
| 2 | pncan3i.2 | |- B e. CC |
|
| 3 | negsub | |- ( ( A e. CC /\ B e. CC ) -> ( A + -u B ) = ( A - B ) ) |
|
| 4 | 1 2 3 | mp2an | |- ( A + -u B ) = ( A - B ) |