Metamath Proof Explorer


Theorem readdcld

Description: Closure law for addition of reals. (Contributed by Mario Carneiro, 27-May-2016)

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

Proof

Step Hyp Ref Expression
1 recnd.1
 |-  ( ph -> A e. RR )
2 readdcld.2
 |-  ( ph -> B e. RR )
3 readdcl
 |-  ( ( A e. RR /\ B e. RR ) -> ( A + B ) e. RR )
4 1 2 3 syl2anc
 |-  ( ph -> ( A + B ) e. RR )