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Theorem ssrdv 3278
 Description: Deduction rule based on subclass definition. (Contributed by NM, 15-Nov-1995.)
Hypothesis
Ref Expression
ssrdv.1
Assertion
Ref Expression
ssrdv
Distinct variable groups:   ,   ,   ,

Proof of Theorem ssrdv
StepHypRef Expression
1 ssrdv.1 . . 3
21alrimiv 1631 . 2
3 dfss2 3262 . 2
42, 3sylibr 203 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1540   wcel 1710   wss 3257 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-ss 3259 This theorem is referenced by:  sscon  3400  ssdif  3401  unss1  3432  ssrin  3480  eq0rdv  3585  uniss  3912  intss1  3941  intmin  3946  intssuni  3948  iunss1  3980  iinss1  3981  ss2iun  3984  ssiun  4008  ssiun2  4009  iinss  4017  iinss2  4018  sspwb  4118  pwadjoin  4119  phi11lem1  4595  phi011lem1  4598  ssrel  4844  dmss  4906  dmcosseq  4973  ssrnres  5059  fun11iun  5305  chfnrn  5399  ffnfv  5427  enadjlem1  6059  enmap2lem5  6067  enmap1lem5  6073  enprmaplem5  6080  enprmaplem6  6081
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