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Theorem reu7 2907
 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 2902 . 2
2 rmo4.1 . . . . . . 7
3 equequ1 1692 . . . . . . . 8
4 equcom 1686 . . . . . . . 8
53, 4bitrdi 195 . . . . . . 7
62, 5imbi12d 233 . . . . . 6
76cbvralv 2680 . . . . 5
87rexbii 2464 . . . 4
9 equequ1 1692 . . . . . . 7
109imbi2d 229 . . . . . 6
1110ralbidv 2457 . . . . 5
1211cbvrexv 2681 . . . 4
138, 12bitri 183 . . 3
1413anbi2i 453 . 2
151, 14bitri 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wral 2435  wrex 2436  wreu 2437 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-reu 2442  df-rmo 2443 This theorem is referenced by: (None)
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