Theorem dfss 2054

Description: A frequently-used variant of subclass definition df-ss 2053.

Assertion

Ref	Expression
dfss	|- (A (_ B <-> A = (A i^i B))

Proof of Theorem dfss

Step	Hyp	Ref	Expression
1		df-ss 2053	. 2 |- (A (_ B <-> (A i^i B) = A)
2		eqcom 1477	. 2 |- ((A i^i B) = A <-> A = (A i^i B))
3	1, 2	bitr 173	1 |- (A (_ B <-> A = (A i^i B))

Syntax hints:   <-> wb 146   = wceq 956   i^i cin 2046   (_ wss 2047

This theorem is referenced by:  dfss2 2058  wefrc 2943  onelin 3103  cnvcnv 3486  funimass1 3572  tz7.44-2 3929  tz7.44-3 3930  frfnom 3951  sbthlem5 4451  abfii2OLD 4562  dmaddpi 5018  dmmulpi 5019  metssba2 7810  mdbr3 10224  mdbr4 10225  ssmd1 10238  stoi 10639

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1469  df-ss 2053

Copyright terms: Public domain