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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 1748 and rspsbc 2991. (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 2920 | . 2 | |
4 | 1, 2, 3 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 wcel 1480 wsbc 2909 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 df-sbc 2910 |
This theorem is referenced by: ovmpodxf 5896 |
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