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Theorem bdsbcALT 14838
Description: Alternate proof of bdsbc 14837. (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 14817 . 2  |- BOUNDED  y  e.  { x  |  ph }
3 df-sbc 2975 . 2  |-  ( [. y  /  x ]. ph  <->  y  e.  { x  |  ph }
)
42, 3bd0r 14804 1  |- BOUNDED  [. y  /  x ]. ph
Colors of variables: wff set class
Syntax hints:    e. wcel 2158   {cab 2173   [.wsbc 2974  BOUNDED wbd 14791
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-bd0 14792  ax-bdsb 14801
This theorem depends on definitions:  df-bi 117  df-clab 2174  df-sbc 2975
This theorem is referenced by: (None)
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