Description: Swap subtrahend and minuend inside the numerator and denominator of a fraction. Deduction form of div2sub . (Contributed by David Moews, 28-Feb-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | div2subd.1 | |- ( ph -> A e. CC ) |
|
| div2subd.2 | |- ( ph -> B e. CC ) |
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| div2subd.3 | |- ( ph -> C e. CC ) |
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| div2subd.4 | |- ( ph -> D e. CC ) |
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| div2subd.5 | |- ( ph -> C =/= D ) |
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| Assertion | div2subd | |- ( ph -> ( ( A - B ) / ( C - D ) ) = ( ( B - A ) / ( D - C ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | div2subd.1 | |- ( ph -> A e. CC ) |
|
| 2 | div2subd.2 | |- ( ph -> B e. CC ) |
|
| 3 | div2subd.3 | |- ( ph -> C e. CC ) |
|
| 4 | div2subd.4 | |- ( ph -> D e. CC ) |
|
| 5 | div2subd.5 | |- ( ph -> C =/= D ) |
|
| 6 | div2sub | |- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC /\ C =/= D ) ) -> ( ( A - B ) / ( C - D ) ) = ( ( B - A ) / ( D - C ) ) ) |
|
| 7 | 1 2 3 4 5 6 | syl23anc | |- ( ph -> ( ( A - B ) / ( C - D ) ) = ( ( B - A ) / ( D - C ) ) ) |