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Theorem syl6eqel 2441
Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl6eqel.1
syl6eqel.2
Assertion
Ref Expression
syl6eqel

Proof of Theorem syl6eqel
StepHypRef Expression
1 syl6eqel.1 . 2
2 syl6eqel.2 . . 3
32a1i 10 . 2
41, 3eqeltrd 2427 1
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1642   wcel 1710
This theorem is referenced by:  syl6eqelr  2442  snex  4111  sikss1c1c  4267  ins2kss  4279  ins3kss  4280  iotaex  4356  eladdc  4398  ssfin  4470  f0cli  5458  elimdelov  5613  ndmovcl  5656  brfns  5859  pprodss4v  5865  muccl  6153  ncaddccl  6165  ceclb  6204  cet  6254  nclenn  6269  nchoicelem12  6300  nchoicelem17  6305  nchoicelem18  6306  nchoicelem19  6307
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349
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