Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdth Structured version   Unicode version

Theorem bdth 9266
Description: A truth (a (closed) theorem) is a bounded formula. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdth.1
Assertion
Ref Expression
bdth BOUNDED

Proof of Theorem bdth
StepHypRef Expression
1 ax-bdeq 9255 . . 3 BOUNDED
21, 1ax-bdim 9249 . 2 BOUNDED
3 id 19 . . 3
4 bdth.1 . . 3
53, 42th 163 . 2
62, 5bd0 9259 1 BOUNDED
Colors of variables: wff set class
Syntax hints:   wi 4  BOUNDED wbd 9247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-bd0 9248  ax-bdim 9249  ax-bdeq 9255
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bdtru  9267  bdcvv  9292
  Copyright terms: Public domain W3C validator