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

Theorem sstr 2947
Description: Transitivity of subclasses. Theorem 6 of [Suppes] p. 23. (Contributed by NM, 5-Sep-2003.)
Assertion
Ref Expression
sstr ((AB B𝐶) → A𝐶)

Proof of Theorem sstr
StepHypRef Expression
1 sstr2 2946 . 2 (AB → (B𝐶A𝐶))
21imp 115 1 ((AB B𝐶) → A𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925
This theorem is referenced by:  sstrd  2949  sylan9ss  2952  ssdifss  3068  uneqin  3182  ssindif0im  3275  undifss  3297  ssrnres  4706  relrelss  4787  fco  4999  fssres  5009  ssimaex  5177  tpostpos2  5821  smores  5848  iccsupr  8585
  Copyright terms: Public domain W3C validator