Description: A composition is not affected by a double converse of its second argument. (Contributed by NM, 8-Oct-2007)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | cocnvcnv2 | |- ( A o. `' `' B ) = ( A o. B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cnvcnv2 | |- `' `' B = ( B |` _V ) |
|
| 2 | 1 | coeq2i | |- ( A o. `' `' B ) = ( A o. ( B |` _V ) ) |
| 3 | resco | |- ( ( A o. B ) |` _V ) = ( A o. ( B |` _V ) ) |
|
| 4 | relco | |- Rel ( A o. B ) |
|
| 5 | dfrel3 | |- ( Rel ( A o. B ) <-> ( ( A o. B ) |` _V ) = ( A o. B ) ) |
|
| 6 | 4 5 | mpbi | |- ( ( A o. B ) |` _V ) = ( A o. B ) |
| 7 | 2 3 6 | 3eqtr2i | |- ( A o. `' `' B ) = ( A o. B ) |