Theorem rexaddd

Description: The extended real addition operation when both arguments are real. Deduction version of rexadd . (Contributed by Glauco Siliprandi, 24-Dec-2020)

	Ref	Expression
Hypotheses	rexaddd.1	|- ( ph -> A e. RR )
	rexaddd.2	|- ( ph -> B e. RR )
Assertion	rexaddd	|- ( ph -> ( A +e B ) = ( A + B ) )

Proof

Step	Hyp	Ref	Expression
1		rexaddd.1	|- ( ph -> A e. RR )
2		rexaddd.2	|- ( ph -> B e. RR )
3		rexadd	|- ( ( A e. RR /\ B e. RR ) -> ( A +e B ) = ( A + B ) )
4	1 2 3	syl2anc	|- ( ph -> ( A +e B ) = ( A + B ) )