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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 3160 | . 2 | |
4 | 2, 3 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1329 cab 2123 wss 3066 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-in 3072 df-ss 3079 |
This theorem is referenced by: ssopab2 4192 iotass 5100 imadif 5198 imain 5200 opabbrex 5808 ssoprab2 5820 tfr1onlemssrecs 6229 tfrcllemssrecs 6242 ss2ixp 6598 |
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