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Mirrors > Home > MPE Home > Th. List > dfco2a | Structured version Visualization version Unicode version |
Description: Generalization of dfco2 5634, where can have any value between and . (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
dfco2a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfco2 5634 | . 2 | |
2 | vex 3203 | . . . . . . . . . . . . . 14 | |
3 | vex 3203 | . . . . . . . . . . . . . . 15 | |
4 | 3 | eliniseg 5494 | . . . . . . . . . . . . . 14 |
5 | 2, 4 | ax-mp 5 | . . . . . . . . . . . . 13 |
6 | 3, 2 | brelrn 5356 | . . . . . . . . . . . . 13 |
7 | 5, 6 | sylbi 207 | . . . . . . . . . . . 12 |
8 | vex 3203 | . . . . . . . . . . . . . 14 | |
9 | 2, 8 | elimasn 5490 | . . . . . . . . . . . . 13 |
10 | 2, 8 | opeldm 5328 | . . . . . . . . . . . . 13 |
11 | 9, 10 | sylbi 207 | . . . . . . . . . . . 12 |
12 | 7, 11 | anim12ci 591 | . . . . . . . . . . 11 |
13 | 12 | adantl 482 | . . . . . . . . . 10 |
14 | 13 | exlimivv 1860 | . . . . . . . . 9 |
15 | elxp 5131 | . . . . . . . . 9 | |
16 | elin 3796 | . . . . . . . . 9 | |
17 | 14, 15, 16 | 3imtr4i 281 | . . . . . . . 8 |
18 | ssel 3597 | . . . . . . . 8 | |
19 | 17, 18 | syl5 34 | . . . . . . 7 |
20 | 19 | pm4.71rd 667 | . . . . . 6 |
21 | 20 | exbidv 1850 | . . . . 5 |
22 | rexv 3220 | . . . . 5 | |
23 | df-rex 2918 | . . . . 5 | |
24 | 21, 22, 23 | 3bitr4g 303 | . . . 4 |
25 | eliun 4524 | . . . 4 | |
26 | eliun 4524 | . . . 4 | |
27 | 24, 25, 26 | 3bitr4g 303 | . . 3 |
28 | 27 | eqrdv 2620 | . 2 |
29 | 1, 28 | syl5eq 2668 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 wrex 2913 cvv 3200 cin 3573 wss 3574 csn 4177 cop 4183 ciun 4520 class class class wbr 4653 cxp 5112 ccnv 5113 cdm 5114 crn 5115 cima 5117 ccom 5118 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-eu 2474 df-mo 2475 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-sbc 3436 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-iun 4522 df-br 4654 df-opab 4713 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 |
This theorem is referenced by: fparlem3 7279 fparlem4 7280 |
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