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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 2822 | . . 3 ⊢ (𝑓 = 𝑔 → ( I ↾ 𝐵) = ( I ↾ 𝐵)) | |
3 | 2 | cbvmptv 5169 | . 2 ⊢ (𝑓 ∈ 𝑇 ↦ ( I ↾ 𝐵)) = (𝑔 ∈ 𝑇 ↦ ( I ↾ 𝐵)) |
4 | 1, 3 | eqtri 2844 | 1 ⊢ 𝑂 = (𝑔 ∈ 𝑇 ↦ ( I ↾ 𝐵)) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ↦ cmpt 5146 I cid 5459 ↾ cres 5557 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rab 3147 df-v 3496 df-dif 3939 df-un 3941 df-in 3943 df-ss 3952 df-nul 4292 df-if 4468 df-sn 4568 df-pr 4570 df-op 4574 df-opab 5129 df-mpt 5147 |
This theorem is referenced by: tendo02 37938 tendo0cl 37941 |
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