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Theorem reu7 2788
 Description: Restricted uniqueness using implicit substitution. (Contributed by NM, 24-Oct-2006.)
Hypothesis
Ref Expression
rmo4.1
Assertion
Ref Expression
reu7
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem reu7
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 reu3 2783 . 2
2 rmo4.1 . . . . . . 7
3 equequ1 1639 . . . . . . . 8
4 equcom 1634 . . . . . . . 8
53, 4syl6bb 194 . . . . . . 7
62, 5imbi12d 232 . . . . . 6
76cbvralv 2578 . . . . 5
87rexbii 2374 . . . 4
9 equequ1 1639 . . . . . . 7
109imbi2d 228 . . . . . 6
1110ralbidv 2369 . . . . 5
1211cbvrexv 2579 . . . 4
138, 12bitri 182 . . 3
1413anbi2i 445 . 2
151, 14bitri 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wral 2349  wrex 2350  wreu 2351 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-reu 2356  df-rmo 2357 This theorem is referenced by: (None)
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