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Theorem reu7 2730
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 2725 . 2
2 rmo4.1 . . . . . . 7
3 equequ1 1595 . . . . . . . 8
4 equcom 1590 . . . . . . . 8
53, 4syl6bb 185 . . . . . . 7
62, 5imbi12d 223 . . . . . 6
76cbvralv 2527 . . . . 5
87rexbii 2325 . . . 4
9 equequ1 1595 . . . . . . 7
109imbi2d 219 . . . . . 6
1110ralbidv 2320 . . . . 5
1211cbvrexv 2528 . . . 4
138, 12bitri 173 . . 3
1413anbi2i 430 . 2
151, 14bitri 173 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wral 2300  wrex 2301  wreu 2302
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-reu 2307  df-rmo 2308
This theorem is referenced by: (None)
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