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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 2566 | . 2 | |
2 | sbcexg 2813 | . . . 4 | |
3 | sbcang 2806 | . . . . . 6 | |
4 | sbcalg 2811 | . . . . . . . . 9 | |
5 | sbcbig 2809 | . . . . . . . . . . 11 | |
6 | sbcg 2827 | . . . . . . . . . . . 12 | |
7 | 6 | bibi1d 222 | . . . . . . . . . . 11 |
8 | 5, 7 | bitrd 177 | . . . . . . . . . 10 |
9 | 8 | albidv 1705 | . . . . . . . . 9 |
10 | 4, 9 | bitrd 177 | . . . . . . . 8 |
11 | abeq2 2146 | . . . . . . . . 9 | |
12 | 11 | sbcbii 2818 | . . . . . . . 8 |
13 | abeq2 2146 | . . . . . . . 8 | |
14 | 10, 12, 13 | 3bitr4g 212 | . . . . . . 7 |
15 | sbcabel.1 | . . . . . . . . 9 | |
16 | 15 | nfcri 2172 | . . . . . . . 8 |
17 | 16 | sbcgf 2825 | . . . . . . 7 |
18 | 14, 17 | anbi12d 442 | . . . . . 6 |
19 | 3, 18 | bitrd 177 | . . . . 5 |
20 | 19 | exbidv 1706 | . . . 4 |
21 | 2, 20 | bitrd 177 | . . 3 |
22 | df-clel 2036 | . . . 4 | |
23 | 22 | sbcbii 2818 | . . 3 |
24 | df-clel 2036 | . . 3 | |
25 | 21, 23, 24 | 3bitr4g 212 | . 2 |
26 | 1, 25 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cab 2026 wnfc 2165 cvv 2557 wsbc 2764 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 |
This theorem is referenced by: csbexga 3885 |
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