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Theorem addcli 7763
Description: Closure law for addition. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1  |-  A  e.  CC
axi.2  |-  B  e.  CC
Assertion
Ref Expression
addcli  |-  ( A  +  B )  e.  CC

Proof of Theorem addcli
StepHypRef Expression
1 axi.1 . 2  |-  A  e.  CC
2 axi.2 . 2  |-  B  e.  CC
3 addcl 7738 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  +  B
)  e.  CC )
41, 2, 3mp2an 422 1  |-  ( A  +  B )  e.  CC
Colors of variables: wff set class
Syntax hints:    e. wcel 1480  (class class class)co 5767   CCcc 7611    + caddc 7616
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addcl 7709
This theorem is referenced by:  negdii  8039  eqneg  8485  nummac  9219  binom2i  10394  3dvds2dec  11552
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