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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 1778 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 1450 | . . 3 |
3 | sbieh.1 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | sbieh.2 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | 2, 4, 6 | sbiedh 1774 | . 2 |
8 | 1, 7 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wsb 1749 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-i9 1517 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-sb 1750 |
This theorem is referenced by: sbie 1778 sbco2vlem 1931 equsb3lem 1937 sbco2yz 1950 dvelimf 2002 elsb3 2142 elsb4 2143 |
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