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Mirrors > Home > ILE Home > Th. List > sbalyz | Unicode version |
Description: Move universal quantifier in and out of substitution. Identical to sbal 1876 except that it has an additional distinct variable constraint on and . (Contributed by Jim Kingdon, 29-Dec-2017.) |
Ref | Expression |
---|---|
sbalyz |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1434 | . . . 4 | |
2 | 1 | nfsbxy 1818 | . . 3 |
3 | ax-4 1400 | . . . 4 | |
4 | 3 | sbimi 1647 | . . 3 |
5 | 2, 4 | alrimi 1415 | . 2 |
6 | sb6 1766 | . . . . 5 | |
7 | 6 | albii 1359 | . . . 4 |
8 | alcom 1367 | . . . 4 | |
9 | 7, 8 | bitri 173 | . . 3 |
10 | nfv 1421 | . . . . . 6 | |
11 | 10 | stdpc5 1476 | . . . . 5 |
12 | 11 | alimi 1344 | . . . 4 |
13 | sb2 1650 | . . . 4 | |
14 | 12, 13 | syl 14 | . . 3 |
15 | 9, 14 | sylbi 114 | . 2 |
16 | 5, 15 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wsb 1645 |
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 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: sbal 1876 |
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