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Mirrors > Home > ILE Home > Th. List > sbabel | Unicode version |
Description: Theorem to move a substitution in and out of a class abstraction. (Contributed by NM, 27-Sep-2003.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
sbabel.1 |
Ref | Expression |
---|---|
sbabel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbex 1979 | . . 3 | |
2 | sban 1928 | . . . . 5 | |
3 | nfv 1508 | . . . . . . . . . 10 | |
4 | 3 | sbf 1750 | . . . . . . . . 9 |
5 | 4 | sbrbis 1934 | . . . . . . . 8 |
6 | 5 | sbalv 1980 | . . . . . . 7 |
7 | abeq2 2248 | . . . . . . . 8 | |
8 | 7 | sbbii 1738 | . . . . . . 7 |
9 | abeq2 2248 | . . . . . . 7 | |
10 | 6, 8, 9 | 3bitr4i 211 | . . . . . 6 |
11 | sbabel.1 | . . . . . . . 8 | |
12 | 11 | nfcri 2275 | . . . . . . 7 |
13 | 12 | sbf 1750 | . . . . . 6 |
14 | 10, 13 | anbi12i 455 | . . . . 5 |
15 | 2, 14 | bitri 183 | . . . 4 |
16 | 15 | exbii 1584 | . . 3 |
17 | 1, 16 | bitri 183 | . 2 |
18 | df-clel 2135 | . . 3 | |
19 | 18 | sbbii 1738 | . 2 |
20 | df-clel 2135 | . 2 | |
21 | 17, 19, 20 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 wsb 1735 cab 2125 wnfc 2268 |
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 |
This theorem is referenced by: (None) |
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