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Theorem ressnop0 6087
 Description: If is not in , then the restriction of a singleton of to is null. (Contributed by Scott Fenton, 15-Apr-2011.)
Assertion
Ref Expression
ressnop0

Proof of Theorem ressnop0
StepHypRef Expression
1 opelxp1 4872 . . 3
21con3i 142 . 2
3 df-res 4851 . . . 4
4 incom 3616 . . . 4
53, 4eqtri 2493 . . 3
6 disjsn 4023 . . . 4
76biimpri 211 . . 3
85, 7syl5eq 2517 . 2
92, 8syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1452   wcel 1904  cvv 3031   cin 3389  c0 3722  csn 3959  cop 3965   cxp 4837   cres 4841 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455  df-xp 4845  df-res 4851 This theorem is referenced by:  fvunsn  6112  fsnunres  6121  wfrlem14  7067  constr3pthlem1  25462  ex-res  25970
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