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Theorem istrg 20960
 Description: Express the predicate " is a topological ring". (Contributed by Mario Carneiro, 5-Oct-2015.)
Hypothesis
Ref Expression
istrg.1 mulGrp
Assertion
Ref Expression
istrg TopMnd

Proof of Theorem istrg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elin 3628 . . 3
21anbi1i 695 . 2 TopMnd TopMnd
3 fveq2 5851 . . . . 5 mulGrp mulGrp
4 istrg.1 . . . . 5 mulGrp
53, 4syl6eqr 2463 . . . 4 mulGrp
65eleq1d 2473 . . 3 mulGrp TopMnd TopMnd
7 df-trg 20956 . . 3 mulGrp TopMnd
86, 7elrab2 3211 . 2 TopMnd
9 df-3an 978 . 2 TopMnd TopMnd
102, 8, 93bitr4i 279 1 TopMnd
 Colors of variables: wff setvar class Syntax hints:   wb 186   wa 369   w3a 976   wceq 1407   wcel 1844   cin 3415  cfv 5571  mulGrpcmgp 17463  crg 17520  TopMndctmd 20863  ctgp 20864  ctrg 20952 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-3an 978  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-rex 2762  df-rab 2765  df-v 3063  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3741  df-if 3888  df-sn 3975  df-pr 3977  df-op 3981  df-uni 4194  df-br 4398  df-iota 5535  df-fv 5579  df-trg 20956 This theorem is referenced by:  trgtmd  20961  trgtgp  20964  trgring  20967  nrgtrg  21492
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