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| Mirrors > Home > ILE Home > Th. List > 3sstr3d | Unicode version | ||
| Description: Substitution of equality into both sides of a subclass relationship. (Contributed by NM, 1-Oct-2000.) |
| Ref | Expression |
|---|---|
| 3sstr3d.1 |
|
| 3sstr3d.2 |
|
| 3sstr3d.3 |
|
| Ref | Expression |
|---|---|
| 3sstr3d |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3sstr3d.1 |
. 2
| |
| 2 | 3sstr3d.2 |
. . 3
| |
| 3 | 3sstr3d.3 |
. . 3
| |
| 4 | 2, 3 | sseq12d 3224 |
. 2
|
| 5 | 1, 4 | mpbid 147 |
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 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-11 1529 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-ext 2187 |
| This theorem depends on definitions: df-bi 117 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-in 3172 df-ss 3179 |
| This theorem is referenced by: fnsnsplitss 5783 |
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