Theorem addid2d 7258

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

Step	Hyp	Ref	Expression
1		muld.1	. 2 |- ( ph -> A e. CC )
2		addid2 7247	. 2 |- ( A e. CC -> ( 0 + A ) = A )
3	1, 2	syl 14	1 |- ( ph -> ( 0 + A ) = A )

Syntax hints:   -> wi 4   = wceq 1284   e. wcel 1433  (class class class)co 5532   CCcc 6979   0cc0 6981   + caddc 6984

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 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467  ax-ext 2063  ax-1cn 7069  ax-icn 7071  ax-addcl 7072  ax-mulcl 7074  ax-addcom 7076  ax-i2m1 7081  ax-0id 7084

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-clel 2077

This theorem is referenced by:  negeu  7299  ltadd2  7523  subge0  7579  sublt0d  7670  un0addcl  8321  lincmb01cmp  9025  modsumfzodifsn  9398  rennim  9888  max0addsup  10105  moddvds  10204  gcdaddm  10375  bezoutlemb  10389