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Theorem moriotass 6582
 Description: Restriction of a unique element to a smaller class. (Contributed by NM, 19-Feb-2006.) (Revised by NM, 16-Jun-2017.)
Assertion
Ref Expression
moriotass
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem moriotass
StepHypRef Expression
1 ssrexv 3410 . . . . 5
21imp 420 . . . 4
323adant3 978 . . 3
4 simp3 960 . . 3
5 reu5 2923 . . 3
63, 4, 5sylanbrc 647 . 2
7 riotass 6581 . 2
86, 7syld3an3 1230 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 937   wceq 1653  wrex 2708  wreu 2709  wrmo 2710   wss 3322  crio 6545 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-rmo 2715  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-riota 6552
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