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Theorem ralss 3502
 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 3433 . . . . 5
21pm4.71rd 633 . . . 4
32imbi1d 315 . . 3
4 impexp 444 . . 3
53, 4syl6bb 261 . 2
65ralbidv2 2836 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   wcel 1840  wral 2751   wss 3411 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1637  ax-4 1650  ax-5 1723  ax-6 1769  ax-7 1812  ax-10 1859  ax-11 1864  ax-12 1876  ax-13 2024  ax-ext 2378 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1406  df-ex 1632  df-nf 1636  df-sb 1762  df-clab 2386  df-cleq 2392  df-clel 2395  df-ral 2756  df-in 3418  df-ss 3425 This theorem is referenced by:  acsfn  15163  acsfn1  15165  acsfn2  15167  mdetunilem9  19304  acsfn1p  35476
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