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Theorem isriscg 26638
 Description: The ring isomorphism relation. (Contributed by Jeff Madsen, 16-Jun-2011.)
Assertion
Ref Expression
isriscg
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem isriscg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq1 2502 . . . 4
21anbi1d 687 . . 3
3 oveq1 6117 . . . . 5
43eleq2d 2509 . . . 4
54exbidv 1637 . . 3
62, 5anbi12d 693 . 2
7 eleq1 2502 . . . 4
87anbi2d 686 . . 3
9 oveq2 6118 . . . . 5
109eleq2d 2509 . . . 4
1110exbidv 1637 . . 3
128, 11anbi12d 693 . 2
13 df-risc 26637 . 2
146, 12, 13brabg 4503 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1727   class class class wbr 4237  (class class class)co 6110  crngo 21994   crngiso 26615   crisc 26616 This theorem is referenced by:  isrisc  26639  risc  26640 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 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-opab 4292  df-iota 5447  df-fv 5491  df-ov 6113  df-risc 26637
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