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Theorem ralss 3565
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:   ,   ,

Proof of Theorem ralss
StepHypRef Expression
1 ssel 3497 . . . . 5
21pm4.71rd 635 . . . 4
32imbi1d 317 . . 3
4 impexp 446 . . 3
53, 4syl6bb 261 . 2
65ralbidv2 2892 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  A.wral 2807  C_wss 3475
This theorem is referenced by:  acsfn  15056  acsfn1  15058  acsfn2  15060  mdetunilem9  19122  acsfn1p  31148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-in 3482  df-ss 3489
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