Description: Rearrangement of 4 terms in a mixed addition and subtraction. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negidd.1 | |- ( ph -> A e. CC ) |
|
pncand.2 | |- ( ph -> B e. CC ) |
||
subaddd.3 | |- ( ph -> C e. CC ) |
||
addsub4d.4 | |- ( ph -> D e. CC ) |
||
Assertion | subadd4d | |- ( ph -> ( ( A - B ) - ( C - D ) ) = ( ( A + D ) - ( B + C ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | |- ( ph -> A e. CC ) |
|
2 | pncand.2 | |- ( ph -> B e. CC ) |
|
3 | subaddd.3 | |- ( ph -> C e. CC ) |
|
4 | addsub4d.4 | |- ( ph -> D e. CC ) |
|
5 | subadd4 | |- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( ( A - B ) - ( C - D ) ) = ( ( A + D ) - ( B + C ) ) ) |
|
6 | 1 2 3 4 5 | syl22anc | |- ( ph -> ( ( A - B ) - ( C - D ) ) = ( ( A + D ) - ( B + C ) ) ) |