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Theorem syl6eleq 2127
Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl6eleq.1
syl6eleq.2  C
Assertion
Ref Expression
syl6eleq  C

Proof of Theorem syl6eleq
StepHypRef Expression
1 syl6eleq.1 . 2
2 syl6eleq.2 . . 3  C
32a1i 9 . 2  C
41, 3eleqtrd 2113 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:  syl6eleqr  2128  prid2g  3466  gt0srpr  6676  eluzel2  8254  fseq1p1m1  8726  fznn0sub2  8755  nn0split  8764  exple1  8964
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