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| Mirrors > Home > ILE Home > Th. List > spsbcd | Unicode version | ||
| Description: Specialization: if a formula is true for all sets, it is true for any class which is a set. Similar to Theorem 6.11 of [Quine] p. 44. See also stdpc4 1797 and rspsbc 3080. (Contributed by Mario Carneiro, 9-Feb-2017.) |
| Ref | Expression |
|---|---|
| spsbcd.1 |
|
| spsbcd.2 |
|
| Ref | Expression |
|---|---|
| spsbcd |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | spsbcd.1 |
. 2
| |
| 2 | spsbcd.2 |
. 2
| |
| 3 | spsbc 3009 |
. 2
| |
| 4 | 1, 2, 3 | sylc 62 |
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 1469 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-sb 1785 df-clab 2191 df-cleq 2197 df-clel 2200 df-v 2773 df-sbc 2998 |
| This theorem is referenced by: ovmpodxf 6070 |
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