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Theorem ralrab2 2844
 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 2423 . . 3
21raleqi 2628 . 2
3 ralab2.1 . . 3
43ralab2 2843 . 2
5 impexp 261 . . . 4
65albii 1446 . . 3
7 df-ral 2419 . . 3
86, 7bitr4i 186 . 2
92, 4, 83bitri 205 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329   wcel 1480  cab 2123  wral 2414  crab 2418 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rab 2423 This theorem is referenced by: (None)
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