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Mirrors > Home > ILE Home > Th. List > addcan2d | Unicode version |
Description: Cancellation law for addition. Theorem I.1 of [Apostol] p. 18. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
addcand.1 | |
addcand.2 | |
addcand.3 |
Ref | Expression |
---|---|
addcan2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | addcand.1 | . 2 | |
2 | addcand.2 | . 2 | |
3 | addcand.3 | . 2 | |
4 | addcan2 7289 | . 2 | |
5 | 1, 2, 3, 4 | syl3anc 1169 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wceq 1284 wcel 1433 (class class class)co 5532 cc 6979 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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-resscn 7068 ax-1cn 7069 ax-icn 7071 ax-addcl 7072 ax-addrcl 7073 ax-mulcl 7074 ax-addcom 7076 ax-addass 7078 ax-distr 7080 ax-i2m1 7081 ax-0id 7084 ax-rnegex 7085 ax-cnre 7087 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 |
This theorem is referenced by: addcan2ad 7295 addneintr2d 7297 nn0opthd 9649 |
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