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Mirrors > Home > ILE Home > Th. List > sb4or | Unicode version |
Description: One direction of a simplified definition of substitution when variables are distinct. Similar to sb4 1713 but stronger in intuitionistic logic. (Contributed by Jim Kingdon, 2-Feb-2018.) |
Ref | Expression |
---|---|
sb4or |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equs5or 1711 | . 2 | |
2 | nfe1 1385 | . . . . . 6 | |
3 | nfa1 1434 | . . . . . 6 | |
4 | 2, 3 | nfim 1464 | . . . . 5 |
5 | 4 | nfri 1412 | . . . 4 |
6 | sb1 1649 | . . . . 5 | |
7 | 6 | imim1i 54 | . . . 4 |
8 | 5, 7 | alrimih 1358 | . . 3 |
9 | 8 | orim2i 678 | . 2 |
10 | 1, 9 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wo 629 wal 1241 wex 1381 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-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: sb4bor 1716 nfsb2or 1718 |
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