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Theorem ralss 3069
 Description: Restricted universal quantification on a subset in terms of superset. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
ralss
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ralss
StepHypRef Expression
1 ssel 3002 . . . . 5
21pm4.71rd 386 . . . 4
32imbi1d 229 . . 3
4 impexp 259 . . 3
53, 4syl6bb 194 . 2
65ralbidv2 2375 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wcel 1434  wral 2353   wss 2982 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-ral 2358  df-in 2988  df-ss 2995 This theorem is referenced by: (None)
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