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Theorem syl6eqss 3077
 Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
syl6eqss.1
syl6eqss.2
Assertion
Ref Expression
syl6eqss

Proof of Theorem syl6eqss
StepHypRef Expression
1 syl6eqss.1 . 2
2 syl6eqss.2 . . 3
32a1i 9 . 2
41, 3eqsstrd 3061 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1290   wss 3000 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-in 3006  df-ss 3013 This theorem is referenced by:  syl6eqssr  3078  resasplitss  5203  fimacnv  5442  en2other2  6883  exmidfodomrlemim  6888  toponsspwpwg  11781  ntrss2  11882  bj-nntrans  12119  nninfsellemsuc  12176
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