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

Theorem eqimssi 3226
Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007.)
Hypothesis
Ref Expression
eqimssi.1  |-  A  =  B
Assertion
Ref Expression
eqimssi  |-  A  C_  B

Proof of Theorem eqimssi
StepHypRef Expression
1 ssid 3190 . 2  |-  A  C_  A
2 eqimssi.1 . 2  |-  A  =  B
31, 2sseqtri 3204 1  |-  A  C_  B
Colors of variables: wff set class
Syntax hints:    = wceq 1364    C_ wss 3144
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157
This theorem is referenced by:  funi  5264  fpr  5715  elfzo1  10215  sumsplitdc  11467  isumlessdc  11531  nconstwlpolem0  15250
  Copyright terms: Public domain W3C validator