Description: Commutative/associative law that swaps the last two terms in a triple sum, rearranging the parentheses. (Contributed by Paul Chapman, 18-May-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | add32r | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A + ( B + C ) ) = ( ( A + C ) + B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addass | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A + B ) + C ) = ( A + ( B + C ) ) ) |
|
2 | add32 | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A + B ) + C ) = ( ( A + C ) + B ) ) |
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3 | 1 2 | eqtr3d | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A + ( B + C ) ) = ( ( A + C ) + B ) ) |