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Mirrors > Home > MPE Home > Th. List > seqeq3d | Structured version Visualization version Unicode version |
Description: Equality deduction for the sequence builder operation. (Contributed by Mario Carneiro, 7-Sep-2013.) |
Ref | Expression |
---|---|
seqeqd.1 |
Ref | Expression |
---|---|
seqeq3d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | seqeqd.1 | . 2 | |
2 | seqeq3 12806 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 cseq 12801 |
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-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 df-iota 5851 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-seq 12802 |
This theorem is referenced by: seqeq123d 12810 seqf1olem2 12841 seqf1o 12842 seqof2 12859 expval 12862 relexp1g 13766 sumeq1 14419 sumeq2w 14422 cbvsum 14425 summo 14448 fsum 14451 geomulcvg 14607 prodeq1f 14638 prodeq2w 14642 prodmo 14666 fprod 14671 gsumvalx 17270 mulgval 17543 gsumval3eu 18305 gsumval3lem2 18307 gsumzres 18310 gsumzf1o 18313 elovolmr 23244 ovolctb 23258 ovoliunlem3 23272 ovoliunnul 23275 ovolshftlem1 23277 voliunlem3 23320 voliun 23322 uniioombllem2 23351 vitalilem4 23380 vitalilem5 23381 dvnfval 23685 mtestbdd 24159 radcnv0 24170 radcnvlt1 24172 radcnvle 24174 psercn 24180 pserdvlem2 24182 abelthlem1 24185 abelthlem3 24187 logtayl 24406 atantayl2 24665 atantayl3 24666 lgamgulm2 24762 lgamcvglem 24766 lgsval 25026 lgsval4 25042 lgsneg 25046 lgsmod 25048 dchrmusumlema 25182 dchrisum0lema 25203 faclim 31632 knoppcnlem9 32491 knoppndvlem4 32506 ovoliunnfl 33451 voliunnfl 33453 radcnvrat 38513 dvradcnv2 38546 binomcxplemcvg 38553 binomcxplemdvsum 38554 binomcxplemnotnn0 38555 sumnnodd 39862 stirlinglem5 40295 sge0isummpt2 40649 ovolval2lem 40857 |
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