Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  reu7 Unicode version

Theorem reu7 3294
 Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.)
Hypothesis
Ref Expression
rmo4.1
Assertion
Ref Expression
reu7
Distinct variable groups:   ,,   ,   ,

Proof of Theorem reu7
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 reu3 3289 . 2
2 rmo4.1 . . . . . . 7
3 equequ1 1798 . . . . . . . 8
4 equcom 1794 . . . . . . . 8
53, 4syl6bb 261 . . . . . . 7
62, 5imbi12d 320 . . . . . 6
76cbvralv 3084 . . . . 5
87rexbii 2959 . . . 4
9 equequ1 1798 . . . . . . 7
109imbi2d 316 . . . . . 6
1110ralbidv 2896 . . . . 5
1211cbvrexv 3085 . . . 4
138, 12bitri 249 . . 3
1413anbi2i 694 . 2
151, 14bitri 249 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wral 2807  E.wrex 2808  E!wreu 2809 This theorem is referenced by:  cshwrepswhash1  14587 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815
 Copyright terms: Public domain W3C validator