Metamath Proof Explorer


Theorem relcnvtrOLD

Description: Obsolete form of relcnvtrg as of 8-Aug-2026. (Contributed by FL, 19-Sep-2011) (Proof shortened by Peter Mazsa, 17-Oct-2023) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion relcnvtrOLD
|- ( Rel R -> ( ( R o. R ) C_ R <-> ( `' R o. `' R ) C_ `' R ) )

Proof

Step Hyp Ref Expression
1 3anidm
 |-  ( ( Rel R /\ Rel R /\ Rel R ) <-> Rel R )
2 relcnvtrgOLD
 |-  ( ( Rel R /\ Rel R /\ Rel R ) -> ( ( R o. R ) C_ R <-> ( `' R o. `' R ) C_ `' R ) )
3 1 2 sylbir
 |-  ( Rel R -> ( ( R o. R ) C_ R <-> ( `' R o. `' R ) C_ `' R ) )