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Theorem bdth 11064
Description: A truth (a (closed) theorem) is a bounded formula. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdth.1  |-  ph
Assertion
Ref Expression
bdth  |- BOUNDED  ph

Proof of Theorem bdth
StepHypRef Expression
1 ax-bdeq 11053 . . 3  |- BOUNDED  x  =  x
21, 1ax-bdim 11047 . 2  |- BOUNDED  ( x  =  x  ->  x  =  x )
3 id 19 . . 3  |-  ( x  =  x  ->  x  =  x )
4 bdth.1 . . 3  |-  ph
53, 42th 172 . 2  |-  ( ( x  =  x  ->  x  =  x )  <->  ph )
62, 5bd0 11057 1  |- BOUNDED  ph
Colors of variables: wff set class
Syntax hints:    -> wi 4  BOUNDED wbd 11045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-ia3 106  ax-bd0 11046  ax-bdim 11047  ax-bdeq 11053
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bdtru  11065  bdcvv  11090
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