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Mirrors > Home > ILE Home > Th. List > ss2abdv | Unicode version |
Description: Deduction of abstraction subclass from implication. (Contributed by NM, 29-Jul-2011.) |
Ref | Expression |
---|---|
ss2abdv.1 |
Ref | Expression |
---|---|
ss2abdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss2abdv.1 | . . 3 | |
2 | 1 | alrimiv 1846 | . 2 |
3 | ss2ab 3165 | . 2 | |
4 | 2, 3 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 cab 2125 wss 3071 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-in 3077 df-ss 3084 |
This theorem is referenced by: ssopab2 4197 iotass 5105 imadif 5203 imain 5205 opabbrex 5815 ssoprab2 5827 tfr1onlemssrecs 6236 tfrcllemssrecs 6249 ss2ixp 6605 |
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