MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcsngOLD Unicode version

Theorem sbcsngOLD 4086
Description: Substitution expressed in terms of quantification over a singleton. (Contributed by NM, 14-Dec-2005.) (Revised by Mario Carneiro, 23-Apr-2015.) Obsolete as of 22-Aug-2018. Use ralsng 4064 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbcsngOLD
Distinct variable group:   ,

Proof of Theorem sbcsngOLD
StepHypRef Expression
1 ralsnsg 4061 . 2
21bicomd 201 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818  A.wral 2807  [.wsbc 3327  {csn 4029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-ral 2812  df-v 3111  df-sbc 3328  df-sn 4030
  Copyright terms: Public domain W3C validator