Theorem rabab 2308

Description: A class abstraction restricted to the universe is unrestricted. (The proof was shortened by Andrew Salmon, 8-Jun-2011.)

Assertion

Ref	Expression
rabab	|- {x e. _V | ph} = {x | ph}

Proof of Theorem rabab

Step	Hyp	Ref	Expression
1		df-rab 2112	. 2 |- {x e. _V | ph} = {x | (x e. _V /\ ph)}
2		visset 2295	. . . 4 |- x e. _V
3	2	biantrur 794	. . 3 |- (ph <-> (x e. _V /\ ph))
4	3	abbii 2006	. 2 |- {x | ph} = {x | (x e. _V /\ ph)}
5	1, 4	eqtr4i 1911	1 |- {x e. _V | ph} = {x | ph}

Syntax hints:   /\ wa 240   = wceq 1298   e. wcel 1300  {cab 1871  {crab 2108  _Vcvv 2292

This theorem is referenced by:  elabs2 2487  intmin2 3244  iunab 3300  euobj1 3834  euobj2 3835  isumclimtfi 8456  fctop 8920  cctop 8922  clsbldneg 14411  euuni2 15663

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-rab 2112  df-v 2294

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