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

Theorem snssd 3509
 Description: The singleton of an element of a class is a subset of the class (deduction rule). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
snssd.1
Assertion
Ref Expression
snssd

Proof of Theorem snssd
StepHypRef Expression
1 snssd.1 . 2
2 snssg 3500 . . 3
31, 2syl 14 . 2
41, 3mpbid 135 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wcel 1393   wss 2917  csn 3375 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-sn 3381 This theorem is referenced by:  ecinxp  6181  xpdom3m  6308  ac6sfi  6352  un0addcl  8215  un0mulcl  8216  fseq1p1m1  8956  bj-omtrans  10081
 Copyright terms: Public domain W3C validator