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Theorem bd3an 12955
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 12940 . . 3  |- BOUNDED  ( ph  /\  ps )
4 bd3or.3 . . 3  |- BOUNDED  ch
53, 4ax-bdan 12940 . 2  |- BOUNDED  ( ( ph  /\  ps )  /\  ch )
6 df-3an 949 . 2  |-  ( (
ph  /\  ps  /\  ch ) 
<->  ( ( ph  /\  ps )  /\  ch )
)
75, 6bd0r 12950 1  |- BOUNDED  ( ph  /\  ps  /\ 
ch )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    /\ w3a 947  BOUNDED wbd 12937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-bd0 12938  ax-bdan 12940
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by: (None)
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