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Theorem bdsbcALT 13046
Description: Alternate proof of bdsbc 13045. (Contributed by BJ, 16-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
bdcsbc.1  |- BOUNDED  ph
Assertion
Ref Expression
bdsbcALT  |- BOUNDED  [. y  /  x ]. ph

Proof of Theorem bdsbcALT
StepHypRef Expression
1 bdcsbc.1 . . 3  |- BOUNDED  ph
21bdab 13025 . 2  |- BOUNDED  y  e.  { x  |  ph }
3 df-sbc 2905 . 2  |-  ( [. y  /  x ]. ph  <->  y  e.  { x  |  ph }
)
42, 3bd0r 13012 1  |- BOUNDED  [. y  /  x ]. ph
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   {cab 2123   [.wsbc 2904  BOUNDED wbd 12999
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 13000  ax-bdsb 13009
This theorem depends on definitions:  df-bi 116  df-clab 2124  df-sbc 2905
This theorem is referenced by: (None)
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