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Theorem sstrid 3108
Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014.)
Hypotheses
Ref Expression
sstrid.1  |-  A  C_  B
sstrid.2  |-  ( ph  ->  B  C_  C )
Assertion
Ref Expression
sstrid  |-  ( ph  ->  A  C_  C )

Proof of Theorem sstrid
StepHypRef Expression
1 sstrid.1 . . 3  |-  A  C_  B
21a1i 9 . 2  |-  ( ph  ->  A  C_  B )
3 sstrid.2 . 2  |-  ( ph  ->  B  C_  C )
42, 3sstrd 3107 1  |-  ( ph  ->  A  C_  C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3071
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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084
This theorem is referenced by:  cossxp2  5062  fimacnv  5549  smores2  6191  f1imaen2g  6687  phplem4dom  6756  isinfinf  6791  fidcenumlemrk  6842  casef  6973  genipv  7324  fzossnn0  9959  seq3split  10259  ctinf  11950  tgcl  12243  epttop  12269  ntrin  12303  cnconst2  12412  cnrest2  12415  cnptopresti  12417  cnptoprest2  12419  hmeores  12494  blin2  12611  ivthdec  12801  limcdifap  12810  limcresi  12814  dvfgg  12836  dvcnp2cntop  12842  dvaddxxbr  12844  reeff1olem  12870
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