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Theorem sseqtri 3191
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 3184 . 2 (𝐴𝐵𝐴𝐶)
41, 3mpbi 145 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wss 3131
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 3137  df-ss 3144
This theorem is referenced by:  sseqtrri  3192  eqimssi  3213  abssi  3232  ssun2  3301  inssddif  3378  difdifdirss  3509  ifidss  3551  pwundifss  4287  unixpss  4741  0ima  4990  sbthlem7  6964  ssnnctlemct  12449  toponsspwpwg  13561  eltg4i  13594  ntrss2  13660  isopn3  13664  tgioo  14085  dvfvalap  14189  dvcnp2cntop  14202
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