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Theorem reu8 2731
Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.)
Hypothesis
Ref Expression
rmo4.1
Assertion
Ref Expression
reu8
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reu8
StepHypRef Expression
1 rmo4.1 . . 3
21cbvreuv 2529 . 2
3 reu6 2724 . 2
4 dfbi2 368 . . . . 5
54ralbii 2324 . . . 4
6 ancom 253 . . . . . 6
7 equcom 1590 . . . . . . . . . 10
87imbi2i 215 . . . . . . . . 9
98ralbii 2324 . . . . . . . 8
109a1i 9 . . . . . . 7
11 biimt 230 . . . . . . . 8
12 df-ral 2305 . . . . . . . . 9
13 bi2.04 237 . . . . . . . . . 10
1413albii 1356 . . . . . . . . 9
15 vex 2554 . . . . . . . . . 10 
_V
16 eleq1 2097 . . . . . . . . . . . . 13
1716, 1imbi12d 223 . . . . . . . . . . . 12
1817bicomd 129 . . . . . . . . . . 11
1918equcoms 1591 . . . . . . . . . 10
2015, 19ceqsalv 2578 . . . . . . . . 9
2112, 14, 203bitrri 196 . . . . . . . 8
2211, 21syl6bb 185 . . . . . . 7
2310, 22anbi12d 442 . . . . . 6
246, 23syl5bb 181 . . . . 5
25 r19.26 2435 . . . . 5
2624, 25syl6rbbr 188 . . . 4
275, 26syl5bb 181 . . 3
2827rexbiia 2333 . 2
292, 3, 283bitri 195 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wcel 1390  wral 2300  wrex 2301  wreu 2302
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-rex 2306  df-reu 2307  df-v 2553
This theorem is referenced by: (None)
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