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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 3242 |
. 2
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3 | abid2 2310 |
. 2
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4 | 2, 3 | sseqtri 3204 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-in 3150 df-ss 3157 |
This theorem is referenced by: ssab2 3254 abf 3481 intab 3888 opabss 4082 relopabi 4770 exse2 5020 mpoexw 6237 tfrlem8 6342 frecabex 6422 fiprc 6840 fival 6998 nqprxx 7574 ltnqex 7577 gtnqex 7578 recexprlemell 7650 recexprlemelu 7651 recexprlempr 7660 4sqlem1 12419 topnex 14038 2sqlem7 14921 |
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