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Theorem 3sstr4d 3072
 Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 30-Nov-1995.) (Proof shortened by Eric Schmidt, 26-Jan-2007.)
Hypotheses
Ref Expression
3sstr4d.1
3sstr4d.2
3sstr4d.3
Assertion
Ref Expression
3sstr4d

Proof of Theorem 3sstr4d
StepHypRef Expression
1 3sstr4d.1 . 2
2 3sstr4d.2 . . 3
3 3sstr4d.3 . . 3
42, 3sseq12d 3058 . 2
51, 4mpbird 166 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1290   wss 3002 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 3008  df-ss 3015 This theorem is referenced by:  rdgss  6164  sucinc2  6223  oawordi  6246  nnnninf  6869  fzoss1  9645  fzoss2  9646  clsss  11881  ntrss  11882  nnsf  12198  nninfself  12208
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