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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 1733 and rspsbc 2963. (Contributed by NM, 16-Jan-2004.) |
Ref | Expression |
---|---|
spsbc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stdpc4 1733 | . . . 4 | |
2 | sbsbc 2886 | . . . 4 | |
3 | 1, 2 | sylib 121 | . . 3 |
4 | dfsbcq 2884 | . . 3 | |
5 | 3, 4 | syl5ib 153 | . 2 |
6 | 5 | vtocleg 2731 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1314 wceq 1316 wcel 1465 wsb 1720 wsbc 2882 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 df-sbc 2883 |
This theorem is referenced by: spsbcd 2894 sbcth 2895 sbcthdv 2896 sbceqal 2936 sbcimdv 2946 csbiebt 3009 csbexga 4026 |
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