Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > esumeq2d | Structured version Visualization version Unicode version |
Description: Equality deduction for extended sum. (Contributed by Thierry Arnoux, 21-Sep-2016.) |
Ref | Expression |
---|---|
esumeq2d.0 | |
esumeq2d.1 |
Ref | Expression |
---|---|
esumeq2d | Σ* Σ* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | esumeq2d.0 | . 2 | |
2 | eqidd 2623 | . 2 | |
3 | esumeq2d.1 | . . 3 | |
4 | 3 | r19.21bi 2932 | . 2 |
5 | 1, 2, 4 | esumeq12dvaf 30093 | 1 Σ* Σ* |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wnf 1708 wral 2912 Σ*cesum 30089 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-iota 5851 df-fv 5896 df-ov 6653 df-esum 30090 |
This theorem is referenced by: esumeq2dv 30100 esumpad 30117 esumlef 30124 esumrnmpt2 30130 voliune 30292 omssubadd 30362 carsggect 30380 omsmeas 30385 dstrvprob 30533 |
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