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

Theorem sseldi 2920
Description: Membership inference from subclass relationship. (Contributed by NM, 25-Jun-2014.)
Hypotheses
Ref Expression
sseli.1 AB
sseldi.2 (φ𝐶 A)
Assertion
Ref Expression
sseldi (φ𝐶 B)

Proof of Theorem sseldi
StepHypRef Expression
1 sseldi.2 . 2 (φ𝐶 A)
2 sseli.1 . . 3 AB
32sseli 2918 . 2 (𝐶 A𝐶 B)
41, 3syl 14 1 (φ𝐶 B)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1374  wss 2894
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908
This theorem is referenced by:  suctr  4108  riotacl  5406  riotasbc  5407  elmpt2cl  5621  ofrval  5645  mpt2xopn0yelv  5776  tpostpos  5801  smores  5829  prarloclemcalc  6356  rexrd  6676
  Copyright terms: Public domain W3C validator