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Theorem addid2d 7395
Description:  0 is a left identity for addition. (Contributed by Mario Carneiro, 27-May-2016.)
Hypothesis
Ref Expression
muld.1  |-  ( ph  ->  A  e.  CC )
Assertion
Ref Expression
addid2d  |-  ( ph  ->  ( 0  +  A
)  =  A )

Proof of Theorem addid2d
StepHypRef Expression
1 muld.1 . 2  |-  ( ph  ->  A  e.  CC )
2 addid2 7384 . 2  |-  ( A  e.  CC  ->  (
0  +  A )  =  A )
31, 2syl 14 1  |-  ( ph  ->  ( 0  +  A
)  =  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    e. wcel 1434  (class class class)co 5564   CCcc 7111   0cc0 7113    + caddc 7116
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2065  ax-1cn 7201  ax-icn 7203  ax-addcl 7204  ax-mulcl 7206  ax-addcom 7208  ax-i2m1 7213  ax-0id 7216
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-clel 2079
This theorem is referenced by:  negeu  7436  ltadd2  7660  subge0  7716  sublt0d  7807  un0addcl  8458  lincmb01cmp  9171  modsumfzodifsn  9548  rennim  10107  max0addsup  10324  moddvds  10430  gcdaddm  10600  bezoutlemb  10614
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