ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqimss2 Unicode version

Theorem eqimss2 3122
Description: Equality implies the subclass relation. (Contributed by NM, 23-Nov-2003.)
Assertion
Ref Expression
eqimss2  |-  ( B  =  A  ->  A  C_  B )

Proof of Theorem eqimss2
StepHypRef Expression
1 eqimss 3121 . 2  |-  ( A  =  B  ->  A  C_  B )
21eqcoms 2120 1  |-  ( B  =  A  ->  A  C_  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316    C_ wss 3041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054
This theorem is referenced by:  disjeq2  3880  disjeq1  3883  poeq2  4192  seeq1  4231  seeq2  4232  dmcoeq  4781  xp11m  4947  funeq  5113  fconst3m  5607  tposeq  6112  undifdcss  6779  ennnfonelemk  11840  ennnfonelemss  11850  qnnen  11871  topgele  12123  topontopn  12131  txdis  12373
  Copyright terms: Public domain W3C validator