Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssdifeq0 Unicode version

Theorem ssdifeq0 3413
 Description: A class is a subclass of itself subtracted from another iff it is the empty set. (Contributed by Steve Rodriguez, 20-Nov-2015.)
Assertion
Ref Expression
ssdifeq0

Proof of Theorem ssdifeq0
StepHypRef Expression
1 inidm 3253 . . 3
2 ssdifin0 3412 . . 3
31, 2syl5eqr 2162 . 2
4 0ss 3369 . . 3
5 id 19 . . . 4
6 difeq2 3156 . . . 4
75, 6sseq12d 3096 . . 3
84, 7mpbiri 167 . 2
93, 8impbii 125 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1314   cdif 3036   cin 3038   wss 3039  c0 3331 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-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rab 2400  df-v 2660  df-dif 3041  df-in 3045  df-ss 3052  df-nul 3332 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator