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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 1921 | . . 3 | |
2 | sban 1870 | . . . . 5 | |
3 | nfv 1461 | . . . . . . . . . 10 | |
4 | 3 | sbf 1700 | . . . . . . . . 9 |
5 | 4 | sbrbis 1876 | . . . . . . . 8 |
6 | 5 | sbalv 1922 | . . . . . . 7 |
7 | abeq2 2187 | . . . . . . . 8 | |
8 | 7 | sbbii 1688 | . . . . . . 7 |
9 | abeq2 2187 | . . . . . . 7 | |
10 | 6, 8, 9 | 3bitr4i 210 | . . . . . 6 |
11 | sbabel.1 | . . . . . . . 8 | |
12 | 11 | nfcri 2213 | . . . . . . 7 |
13 | 12 | sbf 1700 | . . . . . 6 |
14 | 10, 13 | anbi12i 447 | . . . . 5 |
15 | 2, 14 | bitri 182 | . . . 4 |
16 | 15 | exbii 1536 | . . 3 |
17 | 1, 16 | bitri 182 | . 2 |
18 | df-clel 2077 | . . 3 | |
19 | 18 | sbbii 1688 | . 2 |
20 | df-clel 2077 | . 2 | |
21 | 17, 19, 20 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wb 103 wal 1282 wceq 1284 wex 1421 wcel 1433 wsb 1685 cab 2067 wnfc 2206 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 |
This theorem is referenced by: (None) |
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