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Theorem sbt 1709
Description: A substitution into a theorem remains true. (See chvar 1682 and chvarv 1855 for versions using implicit substitition.) (Contributed by NM, 21-Jan-2004.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypothesis
Ref Expression
sbt.1 𝜑
Assertion
Ref Expression
sbt [𝑦 / 𝑥]𝜑

Proof of Theorem sbt
StepHypRef Expression
1 sbt.1 . 2 𝜑
21nfth 1394 . . 3 𝑥𝜑
32sbf 1702 . 2 ([𝑦 / 𝑥]𝜑𝜑)
41, 3mpbir 144 1 [𝑦 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688
This theorem is referenced by:  vjust  2611
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