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Theorem istrg 18185
 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 3522 . . 3
21anbi1i 677 . 2 TopMnd TopMnd
3 fveq2 5720 . . . . 5 mulGrp mulGrp
4 istrg.1 . . . . 5 mulGrp
53, 4syl6eqr 2485 . . . 4 mulGrp
65eleq1d 2501 . . 3 mulGrp TopMnd TopMnd
7 df-trg 18181 . . 3 mulGrp TopMnd
86, 7elrab2 3086 . 2 TopMnd
9 df-3an 938 . 2 TopMnd TopMnd
102, 8, 93bitr4i 269 1 TopMnd
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725   cin 3311  cfv 5446  mulGrpcmgp 15640  crg 15652  TopMndctmd 18092  ctgp 18093  ctrg 18177 This theorem is referenced by:  trgtmd  18186  trgtgp  18189  trgrng  18192  nrgtrg  18717 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-trg 18181
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