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Mirrors > Home > ILE Home > Th. List > sbieh | Unicode version |
Description: Conversion of implicit substitution to explicit substitution. New proofs should use sbie 1674 instead. (Contributed by NM, 30-Jun-1994.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sbieh.1 | |
sbieh.2 |
Ref | Expression |
---|---|
sbieh |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 | |
2 | 1 | hbth 1352 | . . 3 |
3 | sbieh.1 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | sbieh.2 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | 2, 4, 6 | sbiedh 1670 | . 2 |
8 | 1, 7 | ax-mp 7 | 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-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-sb 1646 |
This theorem is referenced by: sbie 1674 sbco2vlem 1820 equsb3lem 1824 sbco2yz 1837 elsb3 1852 elsb4 1853 dvelimf 1891 |
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