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Mirrors > Home > ILE Home > Th. List > sb4bor | Unicode version |
Description: Simplified definition of substitution when variables are distinct, expressed via disjunction. (Contributed by Jim Kingdon, 18-Mar-2018.) |
Ref | Expression |
---|---|
sb4bor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb4or 1714 | . 2 | |
2 | sb2 1650 | . . . . 5 | |
3 | df-bi 110 | . . . . . 6 | |
4 | 3 | simpri 106 | . . . . 5 |
5 | 2, 4 | mpan2 401 | . . . 4 |
6 | 5 | alimi 1344 | . . 3 |
7 | 6 | orim2i 678 | . 2 |
8 | 1, 7 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wo 629 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-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: (None) |
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