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

Theorem sbt 2127
 Description: A substitution into a theorem remains true. (See chvar 1969 and chvarv 1970 for versions using implicit substitution.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
sbt.1
Assertion
Ref Expression
sbt

Proof of Theorem sbt
StepHypRef Expression
1 sbt.1 . 2
21nfth 1563 . . 3
32sbf 2118 . 2
41, 3mpbir 202 1
 Colors of variables: wff set class Syntax hints:  wsb 1659 This theorem is referenced by:  sbie  2150  vjust  2958  iscatd2  13907  iuninc  24012  suppss2f  24050  esumpfinvalf  24467  sbtT  28658  2sb5ndVD  29023  2sb5ndALT  29045 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1660
 Copyright terms: Public domain W3C validator