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

Theorem bdth 9220
Description: A truth (a (closed) theorem) is a bounded formula. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdth.1 φ
Assertion
Ref Expression
bdth BOUNDED φ

Proof of Theorem bdth
StepHypRef Expression
1 ax-bdeq 9209 . . 3 BOUNDED x = x
21, 1ax-bdim 9203 . 2 BOUNDED (x = xx = x)
3 id 19 . . 3 (x = xx = x)
4 bdth.1 . . 3 φ
53, 42th 163 . 2 ((x = xx = x) ↔ φ)
62, 5bd0 9213 1 BOUNDED φ
Colors of variables: wff set class
Syntax hints:  wi 4  BOUNDED wbd 9201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-bd0 9202  ax-bdim 9203  ax-bdeq 9209
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bdtru  9221  bdcvv  9246
  Copyright terms: Public domain W3C validator