Theorem caovcld

Description: Convert an operation closure law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014)

	Ref	Expression
Hypotheses	caovclg.1	|- ( ( ph /\ ( x e. C /\ y e. D ) ) -> ( x F y ) e. E )
	caovcld.2	|- ( ph -> A e. C )
	caovcld.3	|- ( ph -> B e. D )
Assertion	caovcld	|- ( ph -> ( A F B ) e. E )

Proof

Step	Hyp	Ref	Expression
1		caovclg.1	|- ( ( ph /\ ( x e. C /\ y e. D ) ) -> ( x F y ) e. E )
2		caovcld.2	|- ( ph -> A e. C )
3		caovcld.3	|- ( ph -> B e. D )
4		id	|- ( ph -> ph )
5	1	caovclg	|- ( ( ph /\ ( A e. C /\ B e. D ) ) -> ( A F B ) e. E )
6	4 2 3 5	syl12anc	|- ( ph -> ( A F B ) e. E )