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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 28727 | . 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 1528 ∈ wcel 2105 (class class class)co 7145 ℋchba 28623 +ℎ cva 28624 0ℎc0v 28628 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-9 2115 ax-ext 2790 ax-hvcom 28705 ax-hv0cl 28707 ax-hvaddid 28708 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-cleq 2811 |
This theorem is referenced by: hvsubeq0i 28767 hvaddcani 28769 hsn0elch 28952 hhssnv 28968 shscli 29021 |
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