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Mirrors > Home > ILE Home > Th. List > abssdv | Unicode version |
Description: Deduction of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006.) |
Ref | Expression |
---|---|
abssdv.1 |
Ref | Expression |
---|---|
abssdv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abssdv.1 | . . 3 | |
2 | 1 | alrimiv 1830 | . 2 |
3 | abss 3136 | . 2 | |
4 | 2, 3 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1314 wcel 1465 cab 2103 wss 3041 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-in 3047 df-ss 3054 |
This theorem is referenced by: fmpt 5538 tfrlemibacc 6191 tfrlemibfn 6193 tfr1onlembacc 6207 tfr1onlembfn 6209 tfrcllembacc 6220 tfrcllembfn 6222 eroprf 6490 genipv 7285 hashfacen 10547 metrest 12602 |
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