Metamath Proof Explorer

Theorem rnex

Description: The range of a set is a set. Corollary 6.8(3) of TakeutiZaring p. 26. Similar to Lemma 3D of Enderton p. 41. (Contributed by NM, 7-Jul-2008)

Ref Expression
Hypothesis dmex.1
|- A e. _V
Assertion rnex
|- ran A e. _V


Step Hyp Ref Expression
1 dmex.1
 |-  A e. _V
2 rnexg
 |-  ( A e. _V -> ran A e. _V )
3 1 2 ax-mp
 |-  ran A e. _V