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Theorem ralsns 3763
 Description: Substitution expressed in terms of quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.)
Assertion
Ref Expression
ralsns
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem ralsns
StepHypRef Expression
1 sbc6g 3071 . 2
2 df-ral 2619 . . 3
3 elsn 3748 . . . . 5
43imbi1i 315 . . . 4
54albii 1566 . . 3
62, 5bitri 240 . 2
71, 6syl6rbbr 255 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710  wral 2614  wsbc 3046  csn 3737 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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-v 2861  df-sbc 3047  df-sn 3741 This theorem is referenced by:  ralsng  3765  sbcsng  3783
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