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Theorem rexss 3410
 Description: Restricted existential quantification on a subset in terms of superset. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
rexss
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem rexss
StepHypRef Expression
1 ssel 3342 . . . . 5
21pm4.71rd 617 . . . 4
32anbi1d 686 . . 3
4 anass 631 . . 3
53, 4syl6bb 253 . 2
65rexbidv2 2728 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wcel 1725  wrex 2706   wss 3320 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-rex 2711  df-in 3327  df-ss 3334
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