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Theorem sseqtri 3126
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995.)
Hypotheses
Ref Expression
sseqtr.1
sseqtr.2
Assertion
Ref Expression
sseqtri

Proof of Theorem sseqtri
StepHypRef Expression
1 sseqtr.1 . 2
2 sseqtr.2 . . 3
32sseq2i 3119 . 2
41, 3mpbi 144 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   wss 3066 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-in 3072  df-ss 3079 This theorem is referenced by:  sseqtrri  3127  eqimssi  3148  abssi  3167  ssun2  3235  inssddif  3312  difdifdirss  3442  pwundifss  4202  unixpss  4647  0ima  4894  sbthlem7  6844  toponsspwpwg  12178  eltg4i  12213  ntrss2  12279  isopn3  12283  tgioo  12704  dvfvalap  12808  dvcnp2cntop  12821
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