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Theorem eq0rdv 3585
Description: Deduction rule for equality to the empty set. (Contributed by NM, 11-Jul-2014.)
Hypothesis
Ref Expression
eq0rdv.1
Assertion
Ref Expression
eq0rdv
Distinct variable groups:   ,   ,

Proof of Theorem eq0rdv
StepHypRef Expression
1 eq0rdv.1 . . . 4
21pm2.21d 98 . . 3
32ssrdv 3278 . 2
4 ss0 3581 . 2
53, 4syl 15 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wceq 1642   wcel 1710   wss 3257  c0 3550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551
This theorem is referenced by:  tz6.12-2  5346  nchoicelem3  6291
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