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Theorem sbtT 28594
Description: A substitution into a theorem remains true. sbt 2112 with the existence of no virtual hypotheses for the hypothesis expressed as the empty virtual hypothesis collection. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
sbtT.1  |-  (  T. 
->  ph )
Assertion
Ref Expression
sbtT  |-  [ y  /  x ] ph

Proof of Theorem sbtT
StepHypRef Expression
1 sbtT.1 . . 3  |-  (  T. 
->  ph )
21trud 1332 . 2  |-  ph
32sbt 2112 1  |-  [ y  /  x ] ph
Colors of variables: wff set class
Syntax hints:    -> wi 4    T. wtru 1325   [wsb 1658
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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