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Theorem sstrid 3111
Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014.)
Hypotheses
Ref Expression
sstrid.1 𝐴𝐵
sstrid.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
sstrid (𝜑𝐴𝐶)

Proof of Theorem sstrid
StepHypRef Expression
1 sstrid.1 . . 3 𝐴𝐵
21a1i 9 . 2 (𝜑𝐴𝐵)
3 sstrid.2 . 2 (𝜑𝐵𝐶)
42, 3sstrd 3110 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3074
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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3080  df-ss 3087
This theorem is referenced by:  cossxp2  5068  fimacnv  5555  smores2  6197  f1imaen2g  6693  phplem4dom  6762  isinfinf  6797  fidcenumlemrk  6848  casef  6979  genipv  7339  fzossnn0  9981  seq3split  10281  ctinf  11972  tgcl  12265  epttop  12291  ntrin  12325  cnconst2  12434  cnrest2  12437  cnptopresti  12439  cnptoprest2  12441  hmeores  12516  blin2  12633  ivthdec  12823  limcdifap  12832  limcresi  12836  dvfgg  12858  dvcnp2cntop  12864  dvaddxxbr  12866  reeff1olem  12893
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