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Theorem syl5eleq 2123
Description: B membership and equality inference. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl5eleq.1
syl5eleq.2  C
Assertion
Ref Expression
syl5eleq  C

Proof of Theorem syl5eleq
StepHypRef Expression
1 syl5eleq.1 . . 3
21a1i 9 . 2
3 syl5eleq.2 . 2  C
42, 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:  syl5eleqr  2124  opth1  3964  opth  3965  eqelsuc  4122  bj-nnelirr  9413
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