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Theorem sseqtri 3189
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 28-Jul-1995.)
Hypotheses
Ref Expression
sseqtr.1 𝐴𝐵
sseqtr.2 𝐵 = 𝐶
Assertion
Ref Expression
sseqtri 𝐴𝐶

Proof of Theorem sseqtri
StepHypRef Expression
1 sseqtr.1 . 2 𝐴𝐵
2 sseqtr.2 . . 3 𝐵 = 𝐶
32sseq2i 3182 . 2 (𝐴𝐵𝐴𝐶)
41, 3mpbi 145 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  sseqtrri  3190  eqimssi  3211  abssi  3230  ssun2  3299  inssddif  3376  difdifdirss  3507  ifidss  3549  pwundifss  4281  unixpss  4735  0ima  4983  sbthlem7  6955  ssnnctlemct  12417  toponsspwpwg  13153  eltg4i  13188  ntrss2  13254  isopn3  13258  tgioo  13679  dvfvalap  13783  dvcnp2cntop  13796
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