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Theorem sbt 2186
Description: A substitution into a theorem yields a theorem. (See chvar 2040 and chvarv 2041 for versions using implicit substitution.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 20-Jul-2018.)
Hypothesis
Ref Expression
sbt.1  |-  ph
Assertion
Ref Expression
sbt  |-  [ y  /  x ] ph

Proof of Theorem sbt
StepHypRef Expression
1 stdpc4 2118 . 2  |-  ( A. x ph  ->  [ y  /  x ] ph )
2 sbt.1 . 2  |-  ph
31, 2mpg 1641 1  |-  [ y  /  x ] ph
Colors of variables: wff setvar class
Syntax hints:   [wsb 1763
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-12 1878  ax-13 2026
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634  df-sb 1764
This theorem is referenced by:  vjust  3059  iscatd2  15293  iuninc  27844  suppss2f  27906  esumpfinvalf  28509  sbtT  36347  2sb5ndVD  36721  2sb5ndALT  36743
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