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Mirrors > Home > ILE Home > Th. List > spsbc | 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 1748 and rspsbc 2986. (Contributed by NM, 16-Jan-2004.) |
Ref | Expression |
---|---|
spsbc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stdpc4 1748 | . . . 4 | |
2 | sbsbc 2908 | . . . 4 | |
3 | 1, 2 | sylib 121 | . . 3 |
4 | dfsbcq 2906 | . . 3 | |
5 | 3, 4 | syl5ib 153 | . 2 |
6 | 5 | vtocleg 2752 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wceq 1331 wcel 1480 wsb 1735 wsbc 2904 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-v 2683 df-sbc 2905 |
This theorem is referenced by: spsbcd 2916 sbcth 2917 sbcthdv 2918 sbceqal 2959 sbcimdv 2969 csbiebt 3034 csbexga 4051 |
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