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Theorem rexss 3505
 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 3435 . . . . 5
21pm4.71rd 633 . . . 4
32anbi1d 703 . . 3
4 anass 647 . . 3
53, 4syl6bb 261 . 2
65rexbidv2 2913 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   wcel 1842  wrex 2754   wss 3413 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-rex 2759  df-in 3420  df-ss 3427 This theorem is referenced by:  omssubadd  28628
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