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Theorem morex 3283
 Description: Derive membership from uniqueness. (Contributed by Jeff Madsen, 2-Sep-2009.)
Hypotheses
Ref Expression
morex.1
morex.2
Assertion
Ref Expression
morex
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem morex
StepHypRef Expression
1 df-rex 2813 . . . 4
2 exancom 1672 . . . 4
31, 2bitri 249 . . 3
4 nfmo1 2296 . . . . . 6
5 nfe1 1841 . . . . . 6
64, 5nfan 1929 . . . . 5
7 mopick 2356 . . . . 5
86, 7alrimi 1878 . . . 4
9 morex.1 . . . . 5
10 morex.2 . . . . . 6
11 eleq1 2529 . . . . . 6
1210, 11imbi12d 320 . . . . 5
139, 12spcv 3200 . . . 4
148, 13syl 16 . . 3
153, 14sylan2b 475 . 2
1615ancoms 453 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1393   wceq 1395  wex 1613   wcel 1819  wmo 2284  wrex 2808  cvv 3109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111 This theorem is referenced by: (None)
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