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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  |-  ph
Assertion
Ref Expression
sbt  |-  [ y  /  x ] ph

Proof of Theorem sbt
StepHypRef Expression
1 sbt.1 . 2  |-  ph
21nfth 1563 . . 3  |-  F/ x ph
32sbf 2118 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
41, 3mpbir 202 1  |-  [ y  /  x ] ph
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
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