Metamath Proof Explorer


Theorem cnvimarndmOLD

Description: Obsolete version of cnvimarndm as of 29-Sep-2026. (Contributed by Jeff Hankins, 15-Jul-2009) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion cnvimarndmOLD
|- ( `' A " ran A ) = dom A

Proof

Step Hyp Ref Expression
1 imadmrn
 |-  ( `' A " dom `' A ) = ran `' A
2 df-rn
 |-  ran A = dom `' A
3 2 imaeq2i
 |-  ( `' A " ran A ) = ( `' A " dom `' A )
4 dfdm4
 |-  dom A = ran `' A
5 1 3 4 3eqtr4i
 |-  ( `' A " ran A ) = dom A