Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssdif2d Unicode version

Theorem ssdif2d 3082
 Description: If is contained in and is contained in , then is contained in . Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ssdifd.1
ssdif2d.2
Assertion
Ref Expression
ssdif2d

Proof of Theorem ssdif2d
StepHypRef Expression
1 ssdif2d.2 . . 3
21sscond 3080 . 2
3 ssdifd.1 . . 3
43ssdifd 3079 . 2
52, 4sstrd 2955 1
 Colors of variables: wff set class Syntax hints:   wi 4   cdif 2914   wss 2917 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-in1 544  ax-in2 545  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-dif 2920  df-in 2924  df-ss 2931 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator