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Theorem addid2d 7143
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 7132 . 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 1243    e. wcel 1393  (class class class)co 5499   CCcc 6868   0cc0 6870    + caddc 6873
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1cn 6958  ax-icn 6960  ax-addcl 6961  ax-mulcl 6963  ax-addcom 6965  ax-i2m1 6970  ax-0id 6973
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036
This theorem is referenced by:  negeu  7182  ltadd2  7395  subge0  7448  un0addcl  8187  lincmb01cmp  8838  rennim  9478
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