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Theorem sbtT 39285
Description: A substitution into a theorem remains true. sbt 2556 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 (⊤ → 𝜑)
Assertion
Ref Expression
sbtT [𝑦 / 𝑥]𝜑

Proof of Theorem sbtT
StepHypRef Expression
1 sbtT.1 . . 3 (⊤ → 𝜑)
21trud 1642 . 2 𝜑
32sbt 2556 1 [𝑦 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wtru 1633  [wsb 2046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-12 2196  ax-13 2391
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1635  df-ex 1854  df-sb 2047
This theorem is referenced by: (None)
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