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Theorem sstrdi 3109
Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
sstrdi.1 (𝜑𝐴𝐵)
sstrdi.2 𝐵𝐶
Assertion
Ref Expression
sstrdi (𝜑𝐴𝐶)

Proof of Theorem sstrdi
StepHypRef Expression
1 sstrdi.1 . 2 (𝜑𝐴𝐵)
2 sstrdi.2 . . 3 𝐵𝐶
32a1i 9 . 2 (𝜑𝐵𝐶)
41, 3sstrd 3107 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  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:  difss2  3204  sstpr  3684  rintm  3905  eqbrrdva  4709  dmxpss2  4971  rnxpss2  4972  ssxpbm  4974  ssxp1  4975  ssxp2  4976  relfld  5067  funssxp  5292  dff2  5564  fliftf  5700  1stcof  6061  2ndcof  6062  tfrlemibfn  6225  tfr1onlembfn  6241  tfrcllemssrecs  6249  tfrcllembfn  6254  sucinc2  6342  peano5nnnn  7712  peano5nni  8735  suprzclex  9161  ioodisj  9788  fzssnn  9860  fzossnn0  9964  elfzom1elp1fzo  9991  frecuzrdgtcl  10197  frecuzrdgdomlem  10202  frecuzrdgfunlem  10204  zfz1iso  10596  seq3coll  10597  summodclem2a  11162  summodclem2  11163  zsumdc  11165  fsumsersdc  11176  fsum3cvg3  11177  prodmodclem2a  11357  prodmodclem2  11358  exmidunben  11950  strsetsid  12006  lmss  12429  dvbssntrcntop  12836  dvcjbr  12855  reeff1olem  12875  peano5set  13222
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