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Theorem ralss 3410
 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 3343 . . . . 5
21pm4.71rd 618 . . . 4
32imbi1d 310 . . 3
4 impexp 435 . . 3
53, 4syl6bb 254 . 2
65ralbidv2 2728 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wcel 1726  wral 2706   wss 3321 This theorem is referenced by:  acsfn  13885  acsfn1  13887  acsfn2  13889  acsfn1p  27485 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-ral 2711  df-in 3328  df-ss 3335
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