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Theorem bdsbcALT 11238
Description: Alternate proof of bdsbc 11237. (Contributed by BJ, 16-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
bdcsbc.1 BOUNDED 𝜑
Assertion
Ref Expression
bdsbcALT BOUNDED [𝑦 / 𝑥]𝜑

Proof of Theorem bdsbcALT
StepHypRef Expression
1 bdcsbc.1 . . 3 BOUNDED 𝜑
21bdab 11217 . 2 BOUNDED 𝑦 ∈ {𝑥𝜑}
3 df-sbc 2830 . 2 ([𝑦 / 𝑥]𝜑𝑦 ∈ {𝑥𝜑})
42, 3bd0r 11204 1 BOUNDED [𝑦 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wcel 1436  {cab 2071  [wsbc 2829  BOUNDED wbd 11191
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 11192  ax-bdsb 11201
This theorem depends on definitions:  df-bi 115  df-clab 2072  df-sbc 2830
This theorem is referenced by: (None)
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