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Theorem ralab 2997
 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:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem ralab
StepHypRef Expression
1 df-ral 2619 . 2
2 vex 2862 . . . . 5
3 ralab.1 . . . . 5
42, 3elab 2985 . . . 4
54imbi1i 315 . . 3
65albii 1566 . 2
71, 6bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wcel 1710  cab 2339  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861 This theorem is referenced by:  nnadjoinpw  4521  funcnvuni  5161  frds  5935
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