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Theorem sbt 1742
Description: A substitution into a theorem remains true. (See chvar 1715 and chvarv 1889 for versions using implicit substitition.) (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 1425 . . 3  |-  F/ x ph
32sbf 1735 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
41, 3mpbir 145 1  |-  [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:   [wsb 1720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721
This theorem is referenced by:  vjust  2661
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