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Mirrors > Home > ILE Home > Th. List > sbcabel | Unicode version |
Description: Interchange class substitution and class abstraction. (Contributed by NM, 5-Nov-2005.) |
Ref | Expression |
---|---|
sbcabel.1 |
Ref | Expression |
---|---|
sbcabel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2732 | . 2 | |
2 | sbcexg 3000 | . . . 4 | |
3 | sbcang 2989 | . . . . . 6 | |
4 | sbcalg 2998 | . . . . . . . . 9 | |
5 | sbcbig 2992 | . . . . . . . . . . 11 | |
6 | sbcg 3015 | . . . . . . . . . . . 12 | |
7 | 6 | bibi1d 232 | . . . . . . . . . . 11 |
8 | 5, 7 | bitrd 187 | . . . . . . . . . 10 |
9 | 8 | albidv 1811 | . . . . . . . . 9 |
10 | 4, 9 | bitrd 187 | . . . . . . . 8 |
11 | abeq2 2273 | . . . . . . . . 9 | |
12 | 11 | sbcbii 3005 | . . . . . . . 8 |
13 | abeq2 2273 | . . . . . . . 8 | |
14 | 10, 12, 13 | 3bitr4g 222 | . . . . . . 7 |
15 | sbcabel.1 | . . . . . . . . 9 | |
16 | 15 | nfcri 2300 | . . . . . . . 8 |
17 | 16 | sbcgf 3013 | . . . . . . 7 |
18 | 14, 17 | anbi12d 465 | . . . . . 6 |
19 | 3, 18 | bitrd 187 | . . . . 5 |
20 | 19 | exbidv 1812 | . . . 4 |
21 | 2, 20 | bitrd 187 | . . 3 |
22 | df-clel 2160 | . . . 4 | |
23 | 22 | sbcbii 3005 | . . 3 |
24 | df-clel 2160 | . . 3 | |
25 | 21, 23, 24 | 3bitr4g 222 | . 2 |
26 | 1, 25 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wceq 1342 wex 1479 wcel 2135 cab 2150 wnfc 2293 cvv 2721 wsbc 2946 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-sbc 2947 |
This theorem is referenced by: csbexga 4104 |
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