![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsbc | Unicode version |
Description: A formula resulting from proper substitution of a setvar for a setvar in a bounded formula is bounded. See also bdsbcALT 15089. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcsbc.1 |
![]() ![]() |
Ref | Expression |
---|---|
bdsbc |
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsbc.1 |
. . 3
![]() ![]() | |
2 | 1 | ax-bdsb 15052 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | sbsbc 2981 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | bd0 15054 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
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-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-ext 2171 ax-bd0 15043 ax-bdsb 15052 |
This theorem depends on definitions: df-bi 117 df-clab 2176 df-cleq 2182 df-clel 2185 df-sbc 2978 |
This theorem is referenced by: bdccsb 15090 |
Copyright terms: Public domain | W3C validator |