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Theorem reu7 3131
 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 3126 . 2
2 rmo4.1 . . . . . . 7
3 equequ1 1697 . . . . . . . 8
4 equcom 1693 . . . . . . . 8
53, 4syl6bb 254 . . . . . . 7
62, 5imbi12d 313 . . . . . 6
76cbvralv 2934 . . . . 5
87rexbii 2732 . . . 4
9 equequ1 1697 . . . . . . 7
109imbi2d 309 . . . . . 6
1110ralbidv 2727 . . . . 5
1211cbvrexv 2935 . . . 4
138, 12bitri 242 . . 3
1413anbi2i 677 . 2
151, 14bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wral 2707  wrex 2708  wreu 2709 This theorem is referenced by:  cshwssizesame  28322 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-rmo 2715
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