MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbequ2 Unicode version

Theorem sbequ2 1741
Description: An equality theorem for substitution. (Contributed by NM, 16-May-1993.) (Proof shortened by Wolf Lammen, 25-Feb-2018.)
Assertion
Ref Expression
sbequ2

Proof of Theorem sbequ2
StepHypRef Expression
1 df-sb 1740 . . 3
21simplbi 460 . 2
32com12 31 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  E.wex 1612  [wsb 1739
This theorem is referenced by:  stdpc7  1801  sbequ12  1992  dfsb2  2114  sbequi  2116  sbi1  2133  mo3OLD  2324  mopickOLD  2357  2pm13.193  33325  2pm13.193VD  33703
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-sb 1740
  Copyright terms: Public domain W3C validator