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Theorem bdth 7058
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 7047 . . 3 BOUNDED x = x
21, 1ax-bdim 7041 . 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 7051 1 BOUNDED φ
Colors of variables: wff set class
Syntax hints:  wi 4  BOUNDED wbd 7039
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-bd0 7040  ax-bdim 7041  ax-bdeq 7047
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bdtru  7059  bdcvv  7084
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