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Metamath Proof Explorer

Theorem dmcoeq

Description: Domain of a composition. (Contributed by NM, 19-Mar-1998)

		Ref	Expression
	Assertion	dmcoeq	$⊢ dom A = ran B \to dom (A \circ B) = dom B$

Step	Hyp	Ref	Expression
1		eqimss2	$⊢ dom A = ran B \to ran B \subseteq dom A$
2		dmcosseq	$⊢ ran B \subseteq dom A \to dom (A \circ B) = dom B$
3	1 2	syl	$⊢ dom A = ran B \to dom (A \circ B) = dom B$