This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ffrn

Description: A function maps to its range. (Contributed by Glauco Siliprandi, 3-Mar-2021)

		Ref	Expression
	Assertion	ffrn	$⊢ F : A ⟶ B \to F : A ⟶ ran F$

Step	Hyp	Ref	Expression
1		ffn	$⊢ F : A ⟶ B \to F Fn A$
2		dffn3	$⊢ F Fn A \leftrightarrow F : A ⟶ ran F$
3	1 2	sylib	$⊢ F : A ⟶ B \to F : A ⟶ ran F$