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Theorem ralss 3000
Description: Restricted universal quantification on a subset in terms of superset. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
ralss 
C_
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ralss
StepHypRef Expression
1 ssel 2933 . . . . 5 
C_
21pm4.71rd 374 . . . 4 
C_
32imbi1d 220 . . 3 
C_
4 impexp 250 . . 3
53, 4syl6bb 185 . 2 
C_
65ralbidv2 2322 1 
C_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wcel 1390  wral 2300    C_ wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-in 2918  df-ss 2925
This theorem is referenced by: (None)
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