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

Theorem cnvss 4423
Description: Subset theorem for converse. (Contributed by NM, 22-Mar-1998.)
Assertion
Ref Expression
cnvss 
C_  `'  C_  `'

Proof of Theorem cnvss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 2907 . . . 4 
C_  <. ,  >.  <. ,  >.
2 df-br 3728 . . . 4  <. ,  >.
3 df-br 3728 . . . 4  <. ,  >.
41, 2, 33imtr4g 194 . . 3 
C_
54ssopab2dv 3978 . 2 
C_  { <. ,  >.  |  }  C_ 
{ <. , 
>.  |  }
6 df-cnv 4268 . 2  `'  { <. , 
>.  |  }
7 df-cnv 4268 . 2  `'  { <. , 
>.  |  }
85, 6, 73sstr4g 2954 1 
C_  `'  C_  `'
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1366    C_ wss 2885   <.cop 3342   class class class wbr 3727   {copab 3780   `'ccnv 4259
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 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-in 2892  df-ss 2899  df-br 3728  df-opab 3782  df-cnv 4268
This theorem is referenced by:  cnveq  4424  rnss  4479  relcnvtr  4755  funss  4834  funcnvuni  4882  funres11  4885  funcnvres  4886  foimacnv  5057  tposss  5771
  Copyright terms: Public domain W3C validator