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Theorem sbt 1973
Description: A substitution into a theorem remains true. (See chvar 1926 and chvarv 1953 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 1540 . . 3  |-  F/ x ph
32sbf 1966 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
41, 3mpbir 200 1  |-  [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   [wsb 1629
This theorem is referenced by:  vjust  2789  iscatd2  13583  iuninc  23158  suppss2f  23201  esumpfinvalf  23444  sbtT  28336  2sb5ndVD  28686  2sb5ndALT  28709
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630
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