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Mirrors > Home > MPE Home > Th. List > Mathboxes > tendo0cbv | Structured version Visualization version GIF version |
Description: Define additive identity for trace-preserving endomorphisms. Change bound variable to isolate it later. (Contributed by NM, 11-Jun-2013.) |
Ref | Expression |
---|---|
tendo0cbv.o | ⊢ 𝑂 = (𝑓 ∈ 𝑇 ↦ ( I ↾ 𝐵)) |
Ref | Expression |
---|---|
tendo0cbv | ⊢ 𝑂 = (𝑔 ∈ 𝑇 ↦ ( I ↾ 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tendo0cbv.o | . 2 ⊢ 𝑂 = (𝑓 ∈ 𝑇 ↦ ( I ↾ 𝐵)) | |
2 | eqidd 2739 | . . 3 ⊢ (𝑓 = 𝑔 → ( I ↾ 𝐵) = ( I ↾ 𝐵)) | |
3 | 2 | cbvmptv 5133 | . 2 ⊢ (𝑓 ∈ 𝑇 ↦ ( I ↾ 𝐵)) = (𝑔 ∈ 𝑇 ↦ ( I ↾ 𝐵)) |
4 | 1, 3 | eqtri 2761 | 1 ⊢ 𝑂 = (𝑔 ∈ 𝑇 ↦ ( I ↾ 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ↦ cmpt 5110 I cid 5428 ↾ cres 5527 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2162 ax-12 2179 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3an 1090 df-tru 1545 df-ex 1787 df-nf 1791 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-nfc 2881 df-v 3400 df-un 3848 df-sn 4517 df-pr 4519 df-op 4523 df-opab 5093 df-mpt 5111 |
This theorem is referenced by: tendo02 38424 tendo0cl 38427 |
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