Description: The domain and range of a transposition. (Contributed by NM, 10-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | tposf | |- ( F : ( A X. B ) --> C -> tpos F : ( B X. A ) --> C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relxp | |- Rel ( A X. B ) |
|
2 | tposf2 | |- ( Rel ( A X. B ) -> ( F : ( A X. B ) --> C -> tpos F : `' ( A X. B ) --> C ) ) |
|
3 | 1 2 | ax-mp | |- ( F : ( A X. B ) --> C -> tpos F : `' ( A X. B ) --> C ) |
4 | cnvxp | |- `' ( A X. B ) = ( B X. A ) |
|
5 | 4 | feq2i | |- ( tpos F : `' ( A X. B ) --> C <-> tpos F : ( B X. A ) --> C ) |
6 | 3 5 | sylib | |- ( F : ( A X. B ) --> C -> tpos F : ( B X. A ) --> C ) |