Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfss5 GIF version

Theorem dfss5 3142
 Description: Another definition of subclasshood. Similar to df-ss 2931, dfss 2932, and dfss1 3141. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
dfss5 (𝐴𝐵𝐴 = (𝐵𝐴))

Proof of Theorem dfss5
StepHypRef Expression
1 dfss1 3141 . 2 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
2 eqcom 2042 . 2 ((𝐵𝐴) = 𝐴𝐴 = (𝐵𝐴))
31, 2bitri 173 1 (𝐴𝐵𝐴 = (𝐵𝐴))
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1243   ∩ cin 2916   ⊆ 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-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-in 2924  df-ss 2931 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator