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Theorem syl6eleqr 2128
Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005.)
Hypotheses
Ref Expression
syl6eleqr.1
syl6eleqr.2  C
Assertion
Ref Expression
syl6eleqr  C

Proof of Theorem syl6eleqr
StepHypRef Expression
1 syl6eleqr.1 . 2
2 syl6eleqr.2 . . 3  C
32eqcomi 2041 . 2  C
41, 3syl6eleq 2127 1  C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033
This theorem is referenced by:  brelrng  4508  elabrex  5340  fliftel1  5377  ovidig  5560  unielxp  5742  2oconcl  5961  ecopqsi  6097  eroprf  6135  addclnq  6359  mulclnq  6360  recexnq  6374  ltexnqq  6391  prarloclemarch  6401  prarloclemarch2  6402  nnnq  6405  nqnq0  6424  addclnq0  6434  mulclnq0  6435  nqpnq0nq  6436  prarloclemlt  6476  prarloclemlo  6477  prarloclemcalc  6485  nqprm  6525  cauappcvgprlem2  6632  caucvgprlem2  6651  addclsr  6681  mulclsr  6682  pitonnlem2  6743  axaddcl  6750  axmulcl  6752  uztrn2  8266  eluz2nn  8287  peano2uzs  8303
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