Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cbvesumv | Structured version Visualization version GIF version |
Description: Change bound variable in an extended sum. (Contributed by Thierry Arnoux, 19-Jun-2017.) |
Ref | Expression |
---|---|
cbvesum.1 | ⊢ (𝑗 = 𝑘 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
cbvesumv | ⊢ Σ*𝑗 ∈ 𝐴𝐵 = Σ*𝑘 ∈ 𝐴𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvesum.1 | . 2 ⊢ (𝑗 = 𝑘 → 𝐵 = 𝐶) | |
2 | nfcv 2979 | . 2 ⊢ Ⅎ𝑘𝐴 | |
3 | nfcv 2979 | . 2 ⊢ Ⅎ𝑗𝐴 | |
4 | nfcv 2979 | . 2 ⊢ Ⅎ𝑘𝐵 | |
5 | nfcv 2979 | . 2 ⊢ Ⅎ𝑗𝐶 | |
6 | 1, 2, 3, 4, 5 | cbvesum 31303 | 1 ⊢ Σ*𝑗 ∈ 𝐴𝐵 = Σ*𝑘 ∈ 𝐴𝐶 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 Σ*cesum 31288 |
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 2795 |
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 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-uni 4841 df-br 5069 df-opab 5131 df-mpt 5149 df-iota 6316 df-fv 6365 df-ov 7161 df-esum 31289 |
This theorem is referenced by: esumcvg2 31348 omssubadd 31560 totprob 31687 |
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