New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  reu8 Unicode version

Theorem reu8 3032
 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 2837 . 2
3 reu6 3025 . 2
4 dfbi2 609 . . . . 5
54ralbii 2638 . . . 4
6 ancom 437 . . . . . 6
7 equcom 1680 . . . . . . . . . 10
87imbi2i 303 . . . . . . . . 9
98ralbii 2638 . . . . . . . 8
109a1i 10 . . . . . . 7
11 biimt 325 . . . . . . . 8
12 df-ral 2619 . . . . . . . . 9
13 bi2.04 350 . . . . . . . . . 10
1413albii 1566 . . . . . . . . 9
15 vex 2862 . . . . . . . . . 10
16 eleq1 2413 . . . . . . . . . . . . 13
1716, 1imbi12d 311 . . . . . . . . . . . 12
1817bicomd 192 . . . . . . . . . . 11
1918equcoms 1681 . . . . . . . . . 10
2015, 19ceqsalv 2885 . . . . . . . . 9
2112, 14, 203bitrri 263 . . . . . . . 8
2211, 21syl6bb 252 . . . . . . 7
2310, 22anbi12d 691 . . . . . 6
246, 23syl5bb 248 . . . . 5
25 r19.26 2746 . . . . 5
2624, 25syl6rbbr 255 . . . 4
275, 26syl5bb 248 . . 3
2827rexbiia 2647 . 2
292, 3, 283bitri 262 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wceq 1642   wcel 1710  wral 2614  wrex 2615  wreu 2616 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-ral 2619  df-rex 2620  df-reu 2621  df-v 2861 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator