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Theorem isriscg 28961
 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 2526 . . . 4
21anbi1d 704 . . 3
3 oveq1 6210 . . . . 5
43eleq2d 2524 . . . 4
54exbidv 1681 . . 3
62, 5anbi12d 710 . 2
7 eleq1 2526 . . . 4
87anbi2d 703 . . 3
9 oveq2 6211 . . . . 5
109eleq2d 2524 . . . 4
1110exbidv 1681 . . 3
128, 11anbi12d 710 . 2
13 df-risc 28960 . 2
146, 12, 13brabg 4719 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1370  wex 1587   wcel 1758   class class class wbr 4403  (class class class)co 6203  crngo 24041   crngiso 28938   crisc 28939 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pr 4642 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-uni 4203  df-br 4404  df-opab 4462  df-iota 5492  df-fv 5537  df-ov 6206  df-risc 28960 This theorem is referenced by:  isrisc  28962  risc  28963
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