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Theorem sseqtri 2977
 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 2970 . 2 (𝐴𝐵𝐴𝐶)
41, 3mpbi 133 1 𝐴𝐶
 Colors of variables: wff set class Syntax hints:   = wceq 1243   ⊆ wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  sseqtr4i  2978  eqimssi  2999  abssi  3015  ssun2  3107  inssddif  3178  difdifdirss  3307  pwundifss  4022  unixpss  4451  0ima  4685
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