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Metamath Proof Explorer

Theorem fimass

Description: The image of a class under a function with domain and codomain is a subset of its codomain. (Contributed by Glauco Siliprandi, 17-Aug-2020)

		Ref	Expression
	Assertion	fimass	$⊢ F : A ⟶ B \to F [X] \subseteq B$

Proof

Step	Hyp	Ref	Expression
1		imassrn	$⊢ F [X] \subseteq ran F$
2		frn	$⊢ F : A ⟶ B \to ran F \subseteq B$
3	1 2	sstrid	$⊢ F : A ⟶ B \to F [X] \subseteq B$