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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 1775 and rspsbc 3045. (Contributed by NM, 16-Jan-2004.) |
Ref | Expression |
---|---|
spsbc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stdpc4 1775 |
. . . 4
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2 | sbsbc 2966 |
. . . 4
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3 | 1, 2 | sylib 122 |
. . 3
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4 | dfsbcq 2964 |
. . 3
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5 | 3, 4 | imbitrid 154 |
. 2
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6 | 5 | vtocleg 2808 |
1
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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 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-v 2739 df-sbc 2963 |
This theorem is referenced by: spsbcd 2975 sbcth 2976 sbcthdv 2977 sbceqal 3018 sbcimdv 3028 csbiebt 3096 csbexga 4128 |
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