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Theorem moriotass 6286
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:   ,   ,

Proof of Theorem moriotass
StepHypRef Expression
1 ssrexv 3564 . . . . 5
21imp 429 . . . 4
323adant3 1016 . . 3
4 simp3 998 . . 3
5 reu5 3073 . . 3
63, 4, 5sylanbrc 664 . 2
7 riotass 6285 . 2
86, 7syld3an3 1273 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\w3a 973  =wceq 1395  E.wrex 2808  E!wreu 2809  E*wrmo 2810  C_wss 3475  iota_crio 6256
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-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-rmo 2815  df-rab 2816  df-v 3111  df-sbc 3328  df-un 3480  df-in 3482  df-ss 3489  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257
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