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Mirrors > Home > HSE Home > Th. List > hvaddid2i | Structured version Visualization version GIF version |
Description: Addition with the zero vector. (Contributed by NM, 18-Aug-1999.) (New usage is discouraged.) |
Ref | Expression |
---|---|
hvaddid2.1 | ⊢ 𝐴 ∈ ℋ |
Ref | Expression |
---|---|
hvaddid2i | ⊢ (0ℎ +ℎ 𝐴) = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hvaddid2.1 | . 2 ⊢ 𝐴 ∈ ℋ | |
2 | hvaddid2 28806 | . 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 1538 ∈ wcel 2111 (class class class)co 7135 ℋchba 28702 +ℎ cva 28703 0ℎc0v 28707 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-9 2121 ax-ext 2770 ax-hvcom 28784 ax-hv0cl 28786 ax-hvaddid 28787 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-cleq 2791 |
This theorem is referenced by: hvsubeq0i 28846 hvaddcani 28848 hsn0elch 29031 hhssnv 29047 shscli 29100 |
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