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Mirrors > Home > ILE Home > Th. List > unssd | Unicode version |
Description: A deduction showing the union of two subclasses is a subclass. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
unssd.1 |
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unssd.2 |
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Ref | Expression |
---|---|
unssd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unssd.1 |
. 2
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2 | unssd.2 |
. 2
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3 | unss 3311 |
. . 3
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4 | 3 | biimpi 120 |
. 2
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5 | 1, 2, 4 | syl2anc 411 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 |
This theorem is referenced by: tpssi 3761 casef 7089 un0addcl 9211 un0mulcl 9212 fzosplit 10179 fzouzsplit 10181 exmidunben 12429 strleund 12564 lsptpcl 13486 lspun 13493 fsumcncntop 14141 bj-charfun 14644 bj-omtrans 14793 |
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