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 2908 | . 2 ⊢ Ⅎ𝑘𝐴 | |
3 | nfcv 2908 | . 2 ⊢ Ⅎ𝑗𝐴 | |
4 | nfcv 2908 | . 2 ⊢ Ⅎ𝑘𝐵 | |
5 | nfcv 2908 | . 2 ⊢ Ⅎ𝑗𝐶 | |
6 | 1, 2, 3, 4, 5 | cbvesum 31989 | 1 ⊢ Σ*𝑗 ∈ 𝐴𝐵 = Σ*𝑘 ∈ 𝐴𝐶 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1541 Σ*cesum 31974 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1801 ax-4 1815 ax-5 1916 ax-6 1974 ax-7 2014 ax-8 2111 ax-9 2119 ax-10 2140 ax-11 2157 ax-12 2174 ax-ext 2710 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 844 df-3an 1087 df-tru 1544 df-fal 1554 df-ex 1786 df-nf 1790 df-sb 2071 df-clab 2717 df-cleq 2731 df-clel 2817 df-nfc 2890 df-rab 3074 df-v 3432 df-dif 3894 df-un 3896 df-in 3898 df-ss 3908 df-nul 4262 df-if 4465 df-sn 4567 df-pr 4569 df-op 4573 df-uni 4845 df-br 5079 df-opab 5141 df-mpt 5162 df-iota 6388 df-fv 6438 df-ov 7271 df-esum 31975 |
This theorem is referenced by: esumcvg2 32034 omssubadd 32246 totprob 32373 |
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