Theorem dfss5 3205

Description: Another definition of subclasshood. Similar to df-ss 3012, dfss 3013, and dfss1 3204. (Contributed by David Moews, 1-May-2017.)

Assertion

Ref	Expression
dfss5	|- ( A C_ B <-> A = ( B i^i A ) )

Proof of Theorem dfss5

Step	Hyp	Ref	Expression
1		dfss1 3204	. 2 |- ( A C_ B <-> ( B i^i A ) = A )
2		eqcom 2090	. 2 |- ( ( B i^i A ) = A <-> A = ( B i^i A ) )
3	1, 2	bitri 182	1 |- ( A C_ B <-> A = ( B i^i A ) )

Syntax hints:   <-> wb 103   = wceq 1289   i^i cin 2998   C_ wss 2999

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3005  df-ss 3012

This theorem is referenced by: (None)