Metamath Proof Explorer

Theorem fnima

Description: The image of a function's domain is its range. (Contributed by NM, 4-Nov-2004) (Proof shortened by Andrew Salmon, 17-Sep-2011)

Ref Expression
Assertion fnima F Fn A F A = ran F


Step Hyp Ref Expression
1 df-ima F A = ran F A
2 fnresdm F Fn A F A = F
3 2 rneqd F Fn A ran F A = ran F
4 1 3 syl5eq F Fn A F A = ran F