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Theorem bdsbc 9313
Description: A formula resulting from proper substitution of a setvar for a setvar in a bounded formula is bounded. See also bdsbcALT 9314. (Contributed by BJ, 16-Oct-2019.)
Hypothesis
Ref Expression
bdcsbc.1 BOUNDED φ
Assertion
Ref Expression
bdsbc BOUNDED [y / x]φ

Proof of Theorem bdsbc
StepHypRef Expression
1 bdcsbc.1 . . 3 BOUNDED φ
21ax-bdsb 9277 . 2 BOUNDED [y / x]φ
3 sbsbc 2762 . 2 ([y / x]φ[y / x]φ)
42, 3bd0 9279 1 BOUNDED [y / x]φ
Colors of variables: wff set class
Syntax hints:  [wsb 1642  [wsbc 2758  BOUNDED wbd 9267
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9268  ax-bdsb 9277
This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759
This theorem is referenced by:  bdccsb  9315
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