Description: Commutative/associative law that swaps the first two factors in a triple product. (Contributed by NM, 11-May-1999) (Proof shortened by Andrew Salmon, 19-Nov-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | mul.1 | |- A e. CC |
|
| mul.2 | |- B e. CC |
||
| mul.3 | |- C e. CC |
||
| Assertion | mul12i | |- ( A x. ( B x. C ) ) = ( B x. ( A x. C ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mul.1 | |- A e. CC |
|
| 2 | mul.2 | |- B e. CC |
|
| 3 | mul.3 | |- C e. CC |
|
| 4 | mul12 | |- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( A x. ( B x. C ) ) = ( B x. ( A x. C ) ) ) |
|
| 5 | 1 2 3 4 | mp3an | |- ( A x. ( B x. C ) ) = ( B x. ( A x. C ) ) |