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Mirrors > Home > ILE Home > Th. List > addid2 | Unicode version |
Description: is a left identity for addition. (Contributed by Scott Fenton, 3-Jan-2013.) |
Ref | Expression |
---|---|
addid2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0cn 7726 | . . 3 | |
2 | addcom 7867 | . . 3 | |
3 | 1, 2 | mpan2 421 | . 2 |
4 | addid1 7868 | . 2 | |
5 | 3, 4 | eqtr3d 2152 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 (class class class)co 5742 cc 7586 cc0 7588 caddc 7591 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 ax-1cn 7681 ax-icn 7683 ax-addcl 7684 ax-mulcl 7686 ax-addcom 7688 ax-i2m1 7693 ax-0id 7696 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 |
This theorem is referenced by: readdcan 7870 addid2i 7873 addid2d 7880 cnegexlem1 7905 cnegexlem2 7906 addcan 7910 negneg 7980 fzoaddel2 9938 divfl0 10037 modqid 10090 sumrbdclem 11113 summodclem2a 11118 fisum0diag2 11184 eftlub 11323 gcdid 11601 ptolemy 12832 |
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