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Theorem bd3an 11078
Description: A conjunction of three bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd3or.1  |- BOUNDED  ph
bd3or.2  |- BOUNDED  ps
bd3or.3  |- BOUNDED  ch
Assertion
Ref Expression
bd3an  |- BOUNDED  ( ph  /\  ps  /\ 
ch )

Proof of Theorem bd3an
StepHypRef Expression
1 bd3or.1 . . . 4  |- BOUNDED  ph
2 bd3or.2 . . . 4  |- BOUNDED  ps
31, 2ax-bdan 11063 . . 3  |- BOUNDED  ( ph  /\  ps )
4 bd3or.3 . . 3  |- BOUNDED  ch
53, 4ax-bdan 11063 . 2  |- BOUNDED  ( ( ph  /\  ps )  /\  ch )
6 df-3an 924 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
75, 6bd0r 11073 1  |- BOUNDED  ( ph  /\  ps  /\ 
ch )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    /\ w3a 922  BOUNDED wbd 11060
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11061  ax-bdan 11063
This theorem depends on definitions:  df-bi 115  df-3an 924
This theorem is referenced by: (None)
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