Description: The double converse of the restriction of a class. (Contributed by NM, 3-Jun-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | cnvcnvres | |- `' `' ( A |` B ) = ( `' `' A |` B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relres | |- Rel ( A |` B ) |
|
2 | dfrel2 | |- ( Rel ( A |` B ) <-> `' `' ( A |` B ) = ( A |` B ) ) |
|
3 | 1 2 | mpbi | |- `' `' ( A |` B ) = ( A |` B ) |
4 | rescnvcnv | |- ( `' `' A |` B ) = ( A |` B ) |
|
5 | 3 4 | eqtr4i | |- `' `' ( A |` B ) = ( `' `' A |` B ) |