ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl6ss GIF version

Theorem syl6ss 2985
Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
syl6ss.1 (𝜑𝐴𝐵)
syl6ss.2 𝐵𝐶
Assertion
Ref Expression
syl6ss (𝜑𝐴𝐶)

Proof of Theorem syl6ss
StepHypRef Expression
1 syl6ss.1 . 2 (𝜑𝐴𝐵)
2 syl6ss.2 . . 3 𝐵𝐶
32a1i 9 . 2 (𝜑𝐵𝐶)
41, 3sstrd 2983 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  difss2  3100  sstpr  3556  rintm  3772  eqbrrdva  4533  ssxpbm  4784  ssxp1  4785  ssxp2  4786  relfld  4874  funssxp  5088  dff2  5339  fliftf  5467  1stcof  5818  2ndcof  5819  tfrlemibfn  5973  sucinc2  6057  peano5nnnn  7024  peano5nni  7993  ioodisj  8962  fzossnn0  9133  elfzom1elp1fzo  9160  frecuzrdgfn  9362  peano5set  10451  peano5setOLD  10452
  Copyright terms: Public domain W3C validator