Theorem xaddcld

Description: The extended real addition operation is closed in extended reals. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	xnegcld.1	|- ( ph -> A e. RR* )
	xaddcld.2	|- ( ph -> B e. RR* )
Assertion	xaddcld	|- ( ph -> ( A +e B ) e. RR* )

Proof

Step	Hyp	Ref	Expression
1		xnegcld.1	|- ( ph -> A e. RR* )
2		xaddcld.2	|- ( ph -> B e. RR* )
3		xaddcl	|- ( ( A e. RR* /\ B e. RR* ) -> ( A +e B ) e. RR* )
4	1 2 3	syl2anc	|- ( ph -> ( A +e B ) e. RR* )