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Mirrors > Home > ILE Home > Th. List > abssi | Unicode version |
Description: Inference of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006.) |
Ref | Expression |
---|---|
abssi.1 |
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Ref | Expression |
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abssi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abssi.1 |
. . 3
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2 | 1 | ss2abi 3094 |
. 2
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3 | abid2 2209 |
. 2
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4 | 2, 3 | sseqtri 3059 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-in 3006 df-ss 3013 |
This theorem is referenced by: ssab2 3106 abf 3330 intab 3723 opabss 3908 relopabi 4576 exse2 4819 tfrlem8 6097 frecabex 6177 fiprc 6586 nqprxx 7159 ltnqex 7162 gtnqex 7163 recexprlemell 7235 recexprlemelu 7236 recexprlempr 7245 topnex 11840 |
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