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Theorem reu8 3136
 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 2940 . 2
3 reu6 3129 . 2
4 dfbi2 611 . . . . 5
54ralbii 2735 . . . 4
6 ancom 439 . . . . . 6
7 equcom 1694 . . . . . . . . . 10
87imbi2i 305 . . . . . . . . 9
98ralbii 2735 . . . . . . . 8
109a1i 11 . . . . . . 7
11 biimt 327 . . . . . . . 8
12 df-ral 2716 . . . . . . . . 9
13 bi2.04 352 . . . . . . . . . 10
1413albii 1576 . . . . . . . . 9
15 vex 2965 . . . . . . . . . 10
16 eleq1 2502 . . . . . . . . . . . . 13
1716, 1imbi12d 313 . . . . . . . . . . . 12
1817bicomd 194 . . . . . . . . . . 11
1918equcoms 1695 . . . . . . . . . 10
2015, 19ceqsalv 2988 . . . . . . . . 9
2112, 14, 203bitrri 265 . . . . . . . 8
2211, 21syl6bb 254 . . . . . . 7
2310, 22anbi12d 693 . . . . . 6
246, 23syl5bb 250 . . . . 5
25 r19.26 2844 . . . . 5
2624, 25syl6rbbr 257 . . . 4
275, 26syl5bb 250 . . 3
2827rexbiia 2744 . 2
292, 3, 283bitri 264 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wcel 1727  wral 2711  wrex 2712  wreu 2713 This theorem is referenced by:  grpinveu  14870  grpoideu  21828  grpoinveu  21841  cvmlift3lem2  25038  reumodprminv  28285 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-clab 2429  df-cleq 2435  df-clel 2438  df-ral 2716  df-rex 2717  df-reu 2718  df-v 2964
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