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Theorem sseqtri 3032
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 3025 . 2 (𝐴𝐵𝐴𝐶)
41, 3mpbi 143 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1285  wss 2974
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-in 2980  df-ss 2987
This theorem is referenced by:  sseqtr4i  3033  eqimssi  3054  abssi  3070  ssun2  3137  inssddif  3212  difdifdirss  3334  pwundifss  4048  unixpss  4479  0ima  4715
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