ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sstrd GIF version

Theorem sstrd 3035
Description: Subclass transitivity deduction. (Contributed by NM, 2-Jun-2004.)
Hypotheses
Ref Expression
sstrd.1 (𝜑𝐴𝐵)
sstrd.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
sstrd (𝜑𝐴𝐶)

Proof of Theorem sstrd
StepHypRef Expression
1 sstrd.1 . 2 (𝜑𝐴𝐵)
2 sstrd.2 . 2 (𝜑𝐵𝐶)
3 sstr 3033 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 403 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2999
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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012
This theorem is referenced by:  syl5ss  3036  syl6ss  3037  ssdif2d  3139  tfisi  4402  funss  5034  fssxp  5178  fvmptssdm  5387  suppssfv  5852  suppssov1  5853  tposss  6011  tfrlem1  6073  tfrlemibfn  6093  tfr1onlembfn  6109  tfr1onlemubacc  6111  tfr1onlemres  6114  tfrcllembfn  6122  tfrcllemubacc  6124  tfrcllemres  6127  ecinxp  6367  undifdc  6634  sbthlem1  6666  iseqf1olemnab  9917  isumss  10783  strsetsid  11527  strleund  11581  rescncf  11637
  Copyright terms: Public domain W3C validator