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Theorem sbt 2551
Description: A substitution into a theorem yields a theorem. (See chvar 2415 and chvarv 2416 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 𝜑
Assertion
Ref Expression
sbt [𝑦 / 𝑥]𝜑

Proof of Theorem sbt
StepHypRef Expression
1 stdpc4 2483 . 2 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2 sbt.1 . 2 𝜑
31, 2mpg 1896 1 [𝑦 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  [wsb 2067
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220  ax-13 2389
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-sb 2068
This theorem is referenced by:  vjust  3415  iscatd2  16701  iuninc  29922  suppss2f  29984  esumpfinvalf  30679  sbtT  39606  2sb5ndVD  39959  2sb5ndALT  39981
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