Description: Rearrangement of 4 terms in a sum. (Contributed by Mario Carneiro, 27-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | addd.1 | |- ( ph -> A e. CC ) |
|
addd.2 | |- ( ph -> B e. CC ) |
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addd.3 | |- ( ph -> C e. CC ) |
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add4d.4 | |- ( ph -> D e. CC ) |
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Assertion | add4d | |- ( ph -> ( ( A + B ) + ( C + D ) ) = ( ( A + C ) + ( B + D ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addd.1 | |- ( ph -> A e. CC ) |
|
2 | addd.2 | |- ( ph -> B e. CC ) |
|
3 | addd.3 | |- ( ph -> C e. CC ) |
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4 | add4d.4 | |- ( ph -> D e. CC ) |
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5 | add4 | |- ( ( ( A e. CC /\ B e. CC ) /\ ( C e. CC /\ D e. CC ) ) -> ( ( A + B ) + ( C + D ) ) = ( ( A + C ) + ( B + D ) ) ) |
|
6 | 1 2 3 4 5 | syl22anc | |- ( ph -> ( ( A + B ) + ( C + D ) ) = ( ( A + C ) + ( B + D ) ) ) |