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Theorem syl5eleq 2551
Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl5eleq.1
syl5eleq.2
Assertion
Ref Expression
syl5eleq

Proof of Theorem syl5eleq
StepHypRef Expression
1 syl5eleq.1 . . 3
21a1i 11 . 2
3 syl5eleq.2 . 2
42, 3eleqtrd 2547 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818
This theorem is referenced by:  syl5eleqr  2552  opth1  4725  opth  4726  eqelsuc  4964  tfrlem11  7076  oalimcl  7228  omlimcl  7246  frgp0  16778  txdis  20133  ordtconlem1  27906  rankeq1o  29828
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452
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