Metamath Proof Explorer


Theorem fvssunirn

Description: The result of a function value is always a subset of the union of the range, even if it is invalid and thus empty. (Contributed by Stefan O'Rear, 2-Nov-2014) (Revised by Mario Carneiro, 31-Aug-2015) (Proof shortened by SN, 13-Jan-2025)

Ref Expression
Assertion fvssunirn F X ran F

Proof

Step Hyp Ref Expression
1 elfvunirn x F X x ran F
2 1 ssriv F X ran F