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Mirrors > Home > ILE Home > Th. List > sbhypf | Unicode version |
Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf . (Contributed by Raph Levien, 10-Apr-2004.) |
Ref | Expression |
---|---|
sbhypf.1 | |
sbhypf.2 |
Ref | Expression |
---|---|
sbhypf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2560 | . . 3 | |
2 | eqeq1 2046 | . . 3 | |
3 | 1, 2 | ceqsexv 2593 | . 2 |
4 | nfs1v 1815 | . . . 4 | |
5 | sbhypf.1 | . . . 4 | |
6 | 4, 5 | nfbi 1481 | . . 3 |
7 | sbequ12 1654 | . . . . 5 | |
8 | 7 | bicomd 129 | . . . 4 |
9 | sbhypf.2 | . . . 4 | |
10 | 8, 9 | sylan9bb 435 | . . 3 |
11 | 6, 10 | exlimi 1485 | . 2 |
12 | 3, 11 | sylbir 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: mob2 2721 tfisi 4310 ralxpf 4482 rexxpf 4483 nn0ind-raph 8355 |
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