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Theorem sbcsng 3867
 Description: Substitution expressed in terms of quantification over a singleton. (Contributed by NM, 14-Dec-2005.) (Revised by Mario Carneiro, 23-Apr-2015.)
Assertion
Ref Expression
sbcsng
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcsng
StepHypRef Expression
1 ralsns 3846 . 2
21bicomd 194 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wcel 1726  wral 2707  wsbc 3163  csn 3816 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-sbc 3164  df-sn 3822
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