ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  reu8 Structured version   Unicode version

Theorem reu8 2705
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 2504 . 2
3 reu6 2698 . 2
4 dfbi2 368 . . . . 5
54ralbii 2299 . . . 4
6 ancom 253 . . . . . 6
7 equcom 1566 . . . . . . . . . 10
87imbi2i 215 . . . . . . . . 9
98ralbii 2299 . . . . . . . 8
109a1i 9 . . . . . . 7
11 biimt 230 . . . . . . . 8
12 df-ral 2280 . . . . . . . . 9
13 bi2.04 237 . . . . . . . . . 10
1413albii 1332 . . . . . . . . 9
15 vex 2529 . . . . . . . . . 10 
_V
16 eleq1 2073 . . . . . . . . . . . . 13
1716, 1imbi12d 223 . . . . . . . . . . . 12
1817bicomd 129 . . . . . . . . . . 11
1918equcoms 1567 . . . . . . . . . 10
2015, 19ceqsalv 2552 . . . . . . . . 9
2112, 14, 203bitrri 196 . . . . . . . 8
2211, 21syl6bb 185 . . . . . . 7
2310, 22anbi12d 442 . . . . . 6
246, 23syl5bb 181 . . . . 5
25 r19.26 2410 . . . . 5
2624, 25syl6rbbr 188 . . . 4
275, 26syl5bb 181 . . 3
2827rexbiia 2308 . 2
292, 3, 283bitri 195 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1221   wcel 1366  wral 2275  wrex 2276  wreu 2277
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 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-eu 1876  df-clab 2000  df-cleq 2006  df-clel 2009  df-ral 2280  df-rex 2281  df-reu 2282  df-v 2528
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator