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Theorem ralrab2 3002
 Description: Universal quantification over a restricted class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)
Hypothesis
Ref Expression
ralab2.1
Assertion
Ref Expression
ralrab2
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem ralrab2
StepHypRef Expression
1 df-rab 2623 . . 3
21raleqi 2811 . 2
3 ralab2.1 . . 3
43ralab2 3001 . 2
5 impexp 433 . . . 4
65albii 1566 . . 3
7 df-ral 2619 . . 3
86, 7bitr4i 243 . 2
92, 4, 83bitri 262 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wcel 1710  cab 2339  wral 2614  crab 2618 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-rab 2623 This theorem is referenced by: (None)
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