Theorem ralab 3260

Description: Universal quantification over a class abstraction. (Contributed by Jeff Madsen, 10-Jun-2010.)

Hypothesis

Ref	Expression
ralab.1

Assertion

Ref	Expression
ralab

Distinct variable groups:   ,   ,

Proof of Theorem ralab

Step	Hyp	Ref	Expression
1		df-ral 2812	. 2
2		vex 3112	. . . . 5
3		ralab.1	. . . . 5
4	2, 3	elab 3246	. . . 4
5	4	imbi1i 325	. . 3
6	5	albii 1640	. 2
7	1, 6	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  e.wcel 1818  {cab 2442  A.wral 2807

This theorem is referenced by:  ralrnmpt2  6417  funcnvuni  6753  kardex  8333  karden  8334  fimaxre3  10517  ptcnp  20123  ptrescn  20140  itg2leub  22141  nmoubi  25687  nmopub  26827  nmfnleub  26844  nmcexi  26945  mblfinlem3  30053  ismblfin  30055  itg2addnc  30069  hbtlem2  31073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111