Description: Real part distributes over subtraction. (Contributed by Mario Carneiro, 29-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | recld.1 | |- ( ph -> A e. CC ) |
|
readdd.2 | |- ( ph -> B e. CC ) |
||
Assertion | resubd | |- ( ph -> ( Re ` ( A - B ) ) = ( ( Re ` A ) - ( Re ` B ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recld.1 | |- ( ph -> A e. CC ) |
|
2 | readdd.2 | |- ( ph -> B e. CC ) |
|
3 | resub | |- ( ( A e. CC /\ B e. CC ) -> ( Re ` ( A - B ) ) = ( ( Re ` A ) - ( Re ` B ) ) ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( Re ` ( A - B ) ) = ( ( Re ` A ) - ( Re ` B ) ) ) |