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Theorem ressnop0 5905
 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 4903 . . 3
21con3i 129 . 2
3 df-res 4882 . . . 4
4 incom 3525 . . . 4
53, 4eqtri 2455 . . 3
6 disjsn 3860 . . . 4
76biimpri 198 . . 3
85, 7syl5eq 2479 . 2
92, 8syl 16 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1652   wcel 1725  cvv 2948   cin 3311  c0 3620  csn 3806  cop 3809   cxp 4868   cres 4872 This theorem is referenced by:  fvunsn  5917  fsnunres  5926  constr3pthlem1  21634  ex-res  21741  wfrlem14  25543 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876  df-res 4882
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