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| Mirrors > Home > HSE Home > Th. List > hvaddlidi | Structured version Visualization version GIF version | ||
| Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| hvaddlid.1 | ⊢ 𝐴 ∈ ℋ |
| Ref | Expression |
|---|---|
| hvaddlidi | ⊢ (0ℎ +ℎ 𝐴) = 𝐴 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hvaddlid.1 | . 2 ⊢ 𝐴 ∈ ℋ | |
| 2 | hvaddlid 31042 | . 2 ⊢ (𝐴 ∈ ℋ → (0ℎ +ℎ 𝐴) = 𝐴) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (0ℎ +ℎ 𝐴) = 𝐴 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∈ wcel 2108 (class class class)co 7431 ℋchba 30938 +ℎ cva 30939 0ℎc0v 30943 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-9 2118 ax-ext 2708 ax-hvcom 31020 ax-hv0cl 31022 ax-hvaddid 31023 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-cleq 2729 |
| This theorem is referenced by: hvsubeq0i 31082 hvaddcani 31084 hsn0elch 31267 hhssnv 31283 shscli 31336 |
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